Reproducing data utilizing a zero information gain function

ABSTRACT

A method begins by a dispersed storage (DS) processing module receiving a zero information gain (ZIG) encoded data slice and a subset of encoded data slices of a set of encoded data slices. The method continues with the DS processing module generating a set of ZIG encoded data slices using a ZIG function and corresponding ones of the subset of encoded data slices, wherein the set of ZIG encoded data slices represents additional components of recovery information of a first encoded data slice. The method continues with the DS processing module recreating the first encoded data slice from the ZIG encoded data slice and the set of ZIG encoded data slices. The method continues with the DS processing module decoding the subset of encoded data slices and the first encoded data slice using a dispersed storage error coding function to reproduce data.

CROSS REFERENCE TO RELATED PATENTS

The present U.S. Utility patent application claims priority pursuant to35 U.S.C. §119(e) to U.S. Provisional Application No. 61/542,914,entitled “Data Transfer Utilizing Dispersed Storage Encoding”, filedOct. 4, 2011, pending, which is incorporated herein by reference in itsentirety and made part of the present U.S. Utility patent applicationfor all purposes.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not Applicable

INCORPORATION-BY-REFERENCE OF MATERIAL SUBMITTED ON A COMPACT DISC

Not Applicable

BACKGROUND OF THE INVENTION

1. Technical Field of the Invention

This invention relates generally to computing systems and moreparticularly to data storage solutions within such computing systems.

2. Description of Related Art

Computers are known to communicate, process, and store data. Suchcomputers range from wireless smart phones to data centers that supportmillions of web searches, stock trades, or on-line purchases every day.In general, a computing system generates data and/or manipulates datafrom one form into another. For instance, an image sensor of thecomputing system generates raw picture data and, using an imagecompression program (e.g., JPEG, MPEG, etc.), the computing systemmanipulates the raw picture data into a standardized compressed image.

With continued advances in processing speed and communication speed,computers are capable of processing real time multimedia data forapplications ranging from simple voice communications to streaming highdefinition video. As such, general-purpose information appliances arereplacing purpose-built communications devices (e.g., a telephone). Forexample, smart phones can support telephony communications but they arealso capable of text messaging and accessing the internet to performfunctions including email, web browsing, remote applications access, andmedia communications (e.g., telephony voice, image transfer, musicfiles, video files, real time video streaming. etc.).

Each type of computer is constructed and operates in accordance with oneor more communication, processing, and storage standards. As a result ofstandardization and with advances in technology, more and moreinformation content is being converted into digital formats. Forexample, more digital cameras are now being sold than film cameras, thusproducing more digital pictures. As another example, web-basedprogramming is becoming an alternative to over the air televisionbroadcasts and/or cable broadcasts. As further examples, papers, books,video entertainment, home video, etc. are now being stored digitally,which increases the demand on the storage function of computers.

A typical computer storage system includes one or more memory devicesaligned with the needs of the various operational aspects of thecomputer's processing and communication functions. Generally, theimmediacy of access dictates what type of memory device is used. Forexample, random access memory (RAM) memory can be accessed in any randomorder with a constant response time, thus it is typically used for cachememory and main memory. By contrast, memory device technologies thatrequire physical movement such as magnetic disks, tapes, and opticaldiscs, have a variable response time as the physical movement can takelonger than the data transfer, thus they are typically used forsecondary memory (e.g., hard drive, backup memory, etc.).

A computer's storage system will be compliant with one or more computerstorage standards that include, but are not limited to, network filesystem (NFS), flash file system (FFS), disk file system (DFS), smallcomputer system interface (SCSI), internet small computer systeminterface (iSCSI), file transfer protocol (FTP), and web-baseddistributed authoring and versioning (WebDAV). These standards specifythe data storage format (e.g., files, data objects, data blocks,directories, etc.) and interfacing between the computer's processingfunction and its storage system, which is a primary function of thecomputer's memory controller.

Despite the standardization of the computer and its storage system,memory devices fail; especially commercial grade memory devices thatutilize technologies incorporating physical movement (e.g., a discdrive). For example, it is fairly common for a disc drive to routinelysuffer from bit level corruption and to completely fail after threeyears of use. One solution is to a higher-grade disc drive, which addssignificant cost to a computer.

Another solution is to utilize multiple levels of redundant disc drivesto replicate the data into two or more copies. One such redundant driveapproach is called redundant array of independent discs (RAID). In aRAID device, a RAID controller adds parity data to the original databefore storing it across the array. The parity data is calculated fromthe original data such that the failure of a disc will not result in theloss of the original data. For example, RAID 5 uses three discs toprotect data from the failure of a single disc. The parity data, andassociated redundancy overhead data, reduces the storage capacity ofthree independent discs by one third (e.g., n−1=capacity). RAID 6 canrecover from a loss of two discs and requires a minimum of four discswith a storage capacity of n−2.

While RAID addresses the memory device failure issue, it is not withoutits own failures issues that affect its effectiveness, efficiency andsecurity. For instance, as more discs are added to the array, theprobability of a disc failure increases, which increases the demand formaintenance. For example, when a disc fails, it needs to be manuallyreplaced before another disc fails and the data stored in the RAIDdevice is lost. To reduce the risk of data loss, data on a RAID deviceis typically copied on to one or more other RAID devices. While thisaddresses the loss of data issue, it raises a security issue sincemultiple copies of data are available, which increases the chances ofunauthorized access. Further, as the amount of data being stored grows,the overhead of RAID devices becomes a non-trivial efficiency issue.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

FIG. 1 is a schematic block diagram of an embodiment of a computingsystem in accordance with the present invention;

FIG. 2 is a schematic block diagram of an embodiment of a computing corein accordance with the present invention;

FIG. 3 is a schematic block diagram of an embodiment of a distributedstorage processing unit in accordance with the present invention;

FIG. 4 is a schematic block diagram of an embodiment of a grid module inaccordance with the present invention;

FIG. 5 is a diagram of an example embodiment of error coded data slicecreation in accordance with the present invention;

FIG. 6 is another schematic block diagram of an embodiment of acomputing system in accordance with the present invention;

FIG. 7A is a diagram illustrating an example of transforming data intoencoded data in accordance with the present invention;

FIG. 7B is a diagram illustrating another example of transforming datainto encoded data in accordance with the present invention;

FIG. 7C is another schematic block diagram of an embodiment of acomputing system in accordance with the present invention;

FIG. 7D is a flowchart illustrating an example of sending data inaccordance with the present invention;

FIG. 8A is a diagram illustrating an example of transforming encodeddata into data in accordance with the present invention;

FIG. 8B is a diagram illustrating another example of transformingencoded data into data in accordance with the present invention;

FIG. 8C is another schematic block diagram of an embodiment of acomputing system in accordance with the present invention;

FIG. 8D is a flowchart illustrating an example of receiving data inaccordance with the present invention;

FIG. 9A is a diagram illustrating an example of generation of a set ofzero information gain (ZIG) encoded data slices in accordance with thepresent invention;

FIG. 9B is a diagram illustrating another example of generation of a setof zero information gain (ZIG) encoded data slices in accordance withthe present invention;

FIG. 9C is another schematic block diagram of an embodiment of acomputing system in accordance with the present invention;

FIG. 9D is a flowchart illustrating an example generating a set of zeroinformation gain (ZIG) encoded data slices in accordance with thepresent invention;

FIG. 10 is a flowchart illustrating an example of storing encoded datain accordance with the present invention;

FIG. 11 is a flowchart illustrating an example of retrieving encodeddata in accordance with the present invention;

FIG. 12 is a flowchart illustrating an example of determining parametersof an encoding scheme in accordance with the present invention; and

FIG. 13 is a flowchart illustrating an example of rebuilding an encodeddata slice in error in accordance with the present invention.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 is a schematic block diagram of a computing system 10 thatincludes one or more of a first type of user devices 12, one or more ofa second type of user devices 14, at least one distributed storage (DS)processing unit 16, at least one DS managing unit 18, at least onestorage integrity processing unit 20, and a distributed storage network(DSN) memory 22 coupled via a network 24. The network 24 may include oneor more wireless and/or wire lined communication systems; one or moreprivate intranet systems and/or public internet systems; and/or one ormore local area networks (LAN) and/or wide area networks (WAN).

The DSN memory 22 includes a plurality of distributed storage (DS) units36 for storing data of the system. Each of the DS units 36 includes aprocessing module and memory and may be located at a geographicallydifferent site than the other DS units (e.g., one in Chicago, one inMilwaukee, etc.).

Each of the user devices 12-14, the DS processing unit 16, the DSmanaging unit 18, and the storage integrity processing unit 20 may be aportable computing device (e.g., a social networking device, a gamingdevice, a cell phone, a smart phone, a personal digital assistant, adigital music player, a digital video player, a laptop computer, ahandheld computer, a video game controller, and/or any other portabledevice that includes a computing core) and/or a fixed computing device(e.g., a personal computer, a computer server, a cable set-top box, asatellite receiver, a television set, a printer, a fax machine, homeentertainment equipment, a video game console, and/or any type of homeor office computing equipment). Such a portable or fixed computingdevice includes a computing core 26 and one or more interfaces 30, 32,and/or 33. An embodiment of the computing core 26 will be described withreference to FIG. 2.

With respect to the interfaces, each of the interfaces 30, 32, and 33includes software and/or hardware to support one or more communicationlinks via the network 24 indirectly and/or directly. For example,interfaces 30 support a communication link (wired, wireless, direct, viaa LAN, via the network 24, etc.) between the first type of user device14 and the DS processing unit 16. As another example, DSN interface 32supports a plurality of communication links via the network 24 betweenthe DSN memory 22 and the DS processing unit 16, the first type of userdevice 12, and/or the storage integrity processing unit 20. As yetanother example, interface 33 supports a communication link between theDS managing unit 18 and any one of the other devices and/or units 12,14, 16, 20, and/or 22 via the network 24.

In general and with respect to data storage, the system 10 supportsthree primary functions: distributed network data storage management,distributed data storage and retrieval, and data storage integrityverification. In accordance with these three primary functions, data canbe distributedly stored in a plurality of physically different locationsand subsequently retrieved in a reliable and secure manner regardless offailures of individual storage devices, failures of network equipment,the duration of storage, the amount of data being stored, attempts athacking the data, etc.

The DS managing unit 18 performs distributed network data storagemanagement functions, which include establishing distributed datastorage parameters, performing network operations, performing networkadministration, and/or performing network maintenance. The DS managingunit 18 establishes the distributed data storage parameters (e.g.,allocation of virtual DSN memory space, distributed storage parameters,security parameters, billing information, user profile information,etc.) for one or more of the user devices 12-14 (e.g., established forindividual devices, established for a user group of devices, establishedfor public access by the user devices, etc.). For example, the DSmanaging unit 18 coordinates the creation of a vault (e.g., a virtualmemory block) within the DSN memory 22 for a user device (for a group ofdevices, or for public access). The DS managing unit 18 also determinesthe distributed data storage parameters for the vault. In particular,the DS managing unit 18 determines a number of slices (e.g., the numberthat a data segment of a data file and/or data block is partitioned intofor distributed storage) and a read threshold value (e.g., the minimumnumber of slices required to reconstruct the data segment).

As another example, the DS managing module 18 creates and stores,locally or within the DSN memory 22, user profile information. The userprofile information includes one or more of authentication information,permissions, and/or the security parameters. The security parameters mayinclude one or more of encryption/decryption scheme, one or moreencryption keys, key generation scheme, and data encoding/decodingscheme.

As yet another example, the DS managing unit 18 creates billinginformation for a particular user, user group, vault access, publicvault access, etc. For instance, the DS managing unit 18 tracks thenumber of times user accesses a private vault and/or public vaults,which can be used to generate a per-access bill. In another instance,the DS managing unit 18 tracks the amount of data stored and/orretrieved by a user device and/or a user group, which can be used togenerate a per-data-amount bill.

The DS managing unit 18 also performs network operations, networkadministration, and/or network maintenance. As at least part ofperforming the network operations and/or administration, the DS managingunit 18 monitors performance of the devices and/or units of the system10 for potential failures, determines the devices and/or unit'sactivation status, determines the devices' and/or units' loading, andany other system level operation that affects the performance level ofthe system 10. For example, the DS managing unit 18 receives andaggregates network management alarms, alerts, errors, statusinformation, performance information, and messages from the devices12-14 and/or the units 16, 20, 22. For example, the DS managing unit 18receives a simple network management protocol (SNMP) message regardingthe status of the DS processing unit 16.

The DS managing unit 18 performs the network maintenance by identifyingequipment within the system 10 that needs replacing, upgrading,repairing, and/or expanding. For example, the DS managing unit 18determines that the DSN memory 22 needs more DS units 36 or that one ormore of the DS units 36 needs updating.

The second primary function (i.e., distributed data storage andretrieval) begins and ends with a user device 12-14. For instance, if asecond type of user device 14 has a data file 38 and/or data block 40 tostore in the DSN memory 22, it send the data file 38 and/or data block40 to the DS processing unit 16 via its interface 30. As will bedescribed in greater detail with reference to FIG. 2, the interface 30functions to mimic a conventional operating system (OS) file systeminterface (e.g., network file system (NFS), flash file system (FFS),disk file system (DFS), file transfer protocol (FTP), web-baseddistributed authoring and versioning (WebDAV), etc.) and/or a blockmemory interface (e.g., small computer system interface (SCSI), internetsmall computer system interface (iSCSI), etc.). In addition, theinterface 30 may attach a user identification code (ID) to the data file38 and/or data block 40.

The DS processing unit 16 receives the data file 38 and/or data block 40via its interface 30 and performs a distributed storage (DS) process 34thereon (e.g., an error coding dispersal storage function). The DSprocessing 34 begins by partitioning the data file 38 and/or data block40 into one or more data segments, which is represented as Y datasegments. For example, the DS processing 34 may partition the data file38 and/or data block 40 into a fixed byte size segment (e.g., 2¹ to2^(n) bytes, where n=>2) or a variable byte size (e.g., change byte sizefrom segment to segment, or from groups of segments to groups ofsegments, etc.).

For each of the Y data segments, the DS processing 34 error encodes(e.g., forward error correction (FEC), information dispersal algorithm,or error correction coding) and slices (or slices then error encodes)the data segment into a plurality of error coded (EC) data slices 42-48,which is represented as X slices per data segment. The number of slices(X) per segment, which corresponds to a number of pillars n, is set inaccordance with the distributed data storage parameters and the errorcoding scheme. For example, if a Reed-Solomon (or other FEC scheme) isused in an n/k system, then a data segment is divided into n slices,where k number of slices is needed to reconstruct the original data(i.e., k is the threshold). As a few specific examples, the n/k factormay be 5/3; 6/4; 8/6; 8/5; 16/10.

For each slice 42-48, the DS processing unit 16 creates a unique slicename and appends it to the corresponding slice 42-48. The slice nameincludes universal DSN memory addressing routing information (e.g.,virtual memory addresses in the DSN memory 22) and user-specificinformation (e.g., user ID, file name, data block identifier, etc.).

The DS processing unit 16 transmits the plurality of EC slices 42-48 toa plurality of DS units 36 of the DSN memory 22 via the DSN interface 32and the network 24. The DSN interface 32 formats each of the slices fortransmission via the network 24. For example, the DSN interface 32 mayutilize an internet protocol (e.g., TCP/IP, etc.) to packetize theslices 42-48 for transmission via the network 24.

The number of DS units 36 receiving the slices 42-48 is dependent on thedistributed data storage parameters established by the DS managing unit18. For example, the DS managing unit 18 may indicate that each slice isto be stored in a different DS unit 36. As another example, the DSmanaging unit 18 may indicate that like slice numbers of different datasegments are to be stored in the same DS unit 36. For example, the firstslice of each of the data segments is to be stored in a first DS unit36, the second slice of each of the data segments is to be stored in asecond DS unit 36, etc. In this manner, the data is encoded anddistributedly stored at physically diverse locations to improved datastorage integrity and security.

Each DS unit 36 that receives a slice 42-48 for storage translates thevirtual DSN memory address of the slice into a local physical addressfor storage. Accordingly, each DS unit 36 maintains a virtual tophysical memory mapping to assist in the storage and retrieval of data.

The first type of user device 12 performs a similar function to storedata in the DSN memory 22 with the exception that it includes the DSprocessing. As such, the device 12 encodes and slices the data fileand/or data block it has to store. The device then transmits the slices11 to the DSN memory via its DSN interface 32 and the network 24.

For a second type of user device 14 to retrieve a data file or datablock from memory, it issues a read command via its interface 30 to theDS processing unit 16. The DS processing unit 16 performs the DSprocessing 34 to identify the DS units 36 storing the slices of the datafile and/or data block based on the read command. The DS processing unit16 may also communicate with the DS managing unit 18 to verify that theuser device 14 is authorized to access the requested data.

Assuming that the user device is authorized to access the requesteddata, the DS processing unit 16 issues slice read commands to at least athreshold number of the DS units 36 storing the requested data (e.g., toat least 10 DS units for a 16/10 error coding scheme). Each of the DSunits 36 receiving the slice read command, verifies the command,accesses its virtual to physical memory mapping, retrieves the requestedslice, or slices, and transmits it to the DS processing unit 16.

Once the DS processing unit 16 has received a read threshold number ofslices for a data segment, it performs an error decoding function andde-slicing to reconstruct the data segment. When Y number of datasegments has been reconstructed, the DS processing unit 16 provides thedata file 38 and/or data block 40 to the user device 14. Note that thefirst type of user device 12 performs a similar process to retrieve adata file and/or data block.

The storage integrity processing unit 20 performs the third primaryfunction of data storage integrity verification. In general, the storageintegrity processing unit 20 periodically retrieves slices 45, and/orslice names, of a data file or data block of a user device to verifythat one or more slices have not been corrupted or lost (e.g., the DSunit failed). The retrieval process mimics the read process previouslydescribed.

If the storage integrity processing unit 20 determines that one or moreslices is corrupted or lost, it rebuilds the corrupted or lost slice(s)in accordance with the error coding scheme. The storage integrityprocessing unit 20 stores the rebuild slice, or slices, in theappropriate DS unit(s) 36 in a manner that mimics the write processpreviously described.

FIG. 2 is a schematic block diagram of an embodiment of a computing core26 that includes a processing module 50, a memory controller 52, mainmemory 54, a video graphics processing unit 55, an input/output (IO)controller 56, a peripheral component interconnect (PCI) interface 58,at least one IO device interface module 62, a read only memory (ROM)basic input output system (BIOS) 64, and one or more memory interfacemodules. The memory interface module(s) includes one or more of auniversal serial bus (USB) interface module 66, a host bus adapter (HBA)interface module 68, a network interface module 70, a flash interfacemodule 72, a hard drive interface module 74, and a DSN interface module76. Note the DSN interface module 76 and/or the network interface module70 may function as the interface 30 of the user device 14 of FIG. 1.Further note that the IO device interface module 62 and/or the memoryinterface modules may be collectively or individually referred to as IOports.

FIG. 3 is a schematic block diagram of an embodiment of a dispersedstorage (DS) processing module 34 of user device 12 and/or of the DSprocessing unit 16. The DS processing module 34 includes a gatewaymodule 78, an access module 80, a grid module 82, and a storage module84. The DS processing module 34 may also include an interface 30 and theDSnet interface 32 or the interfaces 68 and/or 70 may be part of user 12or of the DS processing unit 14. The DS processing module 34 may furtherinclude a bypass/feedback path between the storage module 84 to thegateway module 78. Note that the modules 78-84 of the DS processingmodule 34 may be in a single unit or distributed across multiple units.

In an example of storing data, the gateway module 78 receives anincoming data object that includes a user ID field 86, an object namefield 88, and the data field 40 and may also receive correspondinginformation that includes a process identifier (e.g., an internalprocess/application ID), metadata, a file system directory, a blocknumber, a transaction message, a user device identity (ID), a dataobject identifier, a source name, and/or user information. The gatewaymodule 78 authenticates the user associated with the data object byverifying the user ID 86 with the managing unit 18 and/or anotherauthenticating unit.

When the user is authenticated, the gateway module 78 obtains userinformation from the management unit 18, the user device, and/or theother authenticating unit. The user information includes a vaultidentifier, operational parameters, and user attributes (e.g., userdata, billing information, etc.). A vault identifier identifies a vault,which is a virtual memory space that maps to a set of DS storage units36. For example, vault 1 (i.e., user 1's DSN memory space) includeseight DS storage units (X=8 wide) and vault 2 (i.e., user 2's DSN memoryspace) includes sixteen DS storage units (X=16 wide). The operationalparameters may include an error coding algorithm, the width n (number ofpillars X or slices per segment for this vault), a read threshold T, awrite threshold, an encryption algorithm, a slicing parameter, acompression algorithm, an integrity check method, caching settings,parallelism settings, and/or other parameters that may be used to accessthe DSN memory layer.

The gateway module 78 uses the user information to assign a source name35 to the data. For instance, the gateway module 60 determines thesource name 35 of the data object 40 based on the vault identifier andthe data object. For example, the source name may contain a fileidentifier (ID), a vault generation number, a reserved field, and avault identifier (ID). As another example, the gateway module 78 maygenerate the file ID based on a hash function of the data object 40.Note that the gateway module 78 may also perform message conversion,protocol conversion, electrical conversion, optical conversion, accesscontrol, user identification, user information retrieval, trafficmonitoring, statistics generation, configuration, management, and/orsource name determination.

The access module 80 receives the data object 40 and creates a series ofdata segments 1 through Y 90-92 in accordance with a data storageprotocol (e.g., file storage system, a block storage system, and/or anaggregated block storage system). The number of segments Y may be chosenor randomly assigned based on a selected segment size and the size ofthe data object. For example, if the number of segments is chosen to bea fixed number, then the size of the segments varies as a function ofthe size of the data object. For instance, if the data object is animage file of 4,194,304 eight bit bytes (e.g., 33,554,432 bits) and thenumber of segments Y=131,072, then each segment is 256 bits or 32 bytes.As another example, if segment sized is fixed, then the number ofsegments Y varies based on the size of data object. For instance, if thedata object is an image file of 4,194,304 bytes and the fixed size ofeach segment is 4,096 bytes, the then number of segments Y=1,024. Notethat each segment is associated with the same source name.

The grid module 82 receives the data segments and may manipulate (e.g.,compression, encryption, cyclic redundancy check (CRC), etc.) each ofthe data segments before performing an error coding function of theerror coding dispersal storage function to produce a pre-manipulateddata segment. After manipulating a data segment, if applicable, the gridmodule 82 error encodes (e.g., Reed-Solomon, Convolution encoding,Trellis encoding, etc.) the data segment or manipulated data segmentinto X error coded data slices 42-44.

The value X, or the number of pillars (e.g., X=16), is chosen as aparameter of the error coding dispersal storage function. Otherparameters of the error coding dispersal function include a readthreshold T, a write threshold W, etc. The read threshold (e.g., T=10,when X=16) corresponds to the minimum number of error-free error codeddata slices required to reconstruct the data segment. In other words,the DS processing module 34 can compensate for X-T (e.g., 16-10=6)missing error coded data slices per data segment. The write threshold Wcorresponds to a minimum number of DS storage units that acknowledgeproper storage of their respective data slices before the DS processingmodule indicates proper storage of the encoded data segment. Note thatthe write threshold is greater than or equal to the read threshold for agiven number of pillars (X).

For each data slice of a data segment, the grid module 82 generates aunique slice name 37 and attaches it thereto. The slice name 37 includesa universal routing information field and a vault specific field and maybe 48 bytes (e.g., 24 bytes for each of the universal routinginformation field and the vault specific field). As illustrated, theuniversal routing information field includes a slice index, a vault ID,a vault generation, and a reserved field. The slice index is based onthe pillar number and the vault ID and, as such, is unique for eachpillar (e.g., slices of the same pillar for the same vault for anysegment will share the same slice index). The vault specific fieldincludes a data name, which includes a file ID and a segment number(e.g., a sequential numbering of data segments 1-Y of a simple dataobject or a data block number).

Prior to outputting the error coded data slices of a data segment, thegrid module may perform post-slice manipulation on the slices. Ifenabled, the manipulation includes slice level compression, encryption,CRC, addressing, tagging, and/or other manipulation to improve theeffectiveness of the computing system.

When the error coded data slices of a data segment are ready to beoutputted, the grid module 82 determines which of the DS storage units36 will store the EC data slices based on a dispersed storage memorymapping associated with the user's vault and/or DS storage unitattributes. The DS storage unit attributes may include availability,self-selection, performance history, link speed, link latency,ownership, available DSN memory, domain, cost, a prioritization scheme,a centralized selection message from another source, a lookup table,data ownership, and/or any other factor to optimize the operation of thecomputing system. Note that the number of DS storage units 36 is equalto or greater than the number of pillars (e.g., X) so that no more thanone error coded data slice of the same data segment is stored on thesame DS storage unit 36. Further note that EC data slices of the samepillar number but of different segments (e.g., EC data slice 1 of datasegment 1 and EC data slice 1 of data segment 2) may be stored on thesame or different DS storage units 36.

The storage module 84 performs an integrity check on the outboundencoded data slices and, when successful, identifies a plurality of DSstorage units based on information provided by the grid module 82. Thestorage module 84 then outputs the encoded data slices 1 through X ofeach segment 1 through Y to the DS storage units 36. Each of the DSstorage units 36 stores its EC data slice(s) and maintains a localvirtual DSN address to physical location table to convert the virtualDSN address of the EC data slice(s) into physical storage addresses.

In an example of a read operation, the user device 12 and/or 14 sends aread request to the DS processing unit 14, which authenticates therequest. When the request is authentic, the DS processing unit 14 sendsa read message to each of the DS storage units 36 storing slices of thedata object being read. The slices are received via the DSnet interface32 and processed by the storage module 84, which performs a parity checkand provides the slices to the grid module 82 when the parity check wassuccessful. The grid module 82 decodes the slices in accordance with theerror coding dispersal storage function to reconstruct the data segment.The access module 80 reconstructs the data object from the data segmentsand the gateway module 78 formats the data object for transmission tothe user device.

FIG. 4 is a schematic block diagram of an embodiment of a grid module 82that includes a control unit 73, a pre-slice manipulator 75, an encoder77, a slicer 79, a post-slice manipulator 81, a pre-slice de-manipulator83, a decoder 85, a de-slicer 87, and/or a post-slice de-manipulator 89.Note that the control unit 73 may be partially or completely external tothe grid module 82. For example, the control unit 73 may be part of thecomputing core at a remote location, part of a user device, part of theDS managing unit 18, or distributed amongst one or more DS storageunits.

In an example of write operation, the pre-slice manipulator 75 receivesa data segment 90-92 and a write instruction from an authorized userdevice. The pre-slice manipulator 75 determines if pre-manipulation ofthe data segment 90-92 is required and, if so, what type. The pre-slicemanipulator 75 may make the determination independently or based oninstructions from the control unit 73, where the determination is basedon a computing system-wide predetermination, a table lookup, vaultparameters associated with the user identification, the type of data,security requirements, available DSN memory, performance requirements,and/or other metadata.

Once a positive determination is made, the pre-slice manipulator 75manipulates the data segment 90-92 in accordance with the type ofmanipulation. For example, the type of manipulation may be compression(e.g., Lempel-Ziv-Welch, Huffman, Golomb, fractal, wavelet, etc.),signatures (e.g., Digital Signature Algorithm (DSA), Elliptic Curve DSA,Secure Hash Algorithm, etc.), watermarking, tagging, encryption (e.g.,Data Encryption Standard, Advanced Encryption Standard, etc.), addingmetadata (e.g., time/date stamping, user information, file type, etc.),cyclic redundancy check (e.g., CRC32), and/or other data manipulationsto produce the pre-manipulated data segment.

The encoder 77 encodes the pre-manipulated data segment 92 using aforward error correction (FEC) encoder (and/or other type of erasurecoding and/or error coding) to produce an encoded data segment 94. Theencoder 77 determines which forward error correction algorithm to usebased on a predetermination associated with the user's vault, a timebased algorithm, user direction, DS managing unit direction, controlunit direction, as a function of the data type, as a function of thedata segment 92 metadata, and/or any other factor to determine algorithmtype. The forward error correction algorithm may be Golay,Multidimensional parity, Reed-Solomon, Hamming, Bose Ray ChauduriHocquenghem (BCH), Cauchy-Reed-Solomon, or any other FEC encoder. Notethat the encoder 77 may use a different encoding algorithm for each datasegment 92, the same encoding algorithm for the data segments 92 of adata object, or a combination thereof.

The encoded data segment 94 is of greater size than the data segment 92by the overhead rate of the encoding algorithm by a factor of X/T, whereX is the width or number of slices, and T is the read threshold. In thisregard, the corresponding decoding process can accommodate at most X−Tmissing EC data slices and still recreate the data segment 92. Forexample, if X=16 and T=10, then the data segment 92 will be recoverableas long as 10 or more EC data slices per segment are not corrupted.

The slicer 79 transforms the encoded data segment 94 into EC data slicesin accordance with the slicing parameter from the vault for this userand/or data segment 92. For example, if the slicing parameter is X=16,then the slicer 79 slices each encoded data segment 94 into 16 encodedslices.

The post-slice manipulator 81 performs, if enabled, post-manipulation onthe encoded slices to produce the EC data slices. If enabled, thepost-slice manipulator 81 determines the type of post-manipulation,which may be based on a computing system-wide predetermination,parameters in the vault for this user, a table lookup, the useridentification, the type of data, security requirements, available DSNmemory, performance requirements, control unit directed, and/or othermetadata. Note that the type of post-slice manipulation may includeslice level compression, signatures, encryption, CRC, addressing,watermarking, tagging, adding metadata, and/or other manipulation toimprove the effectiveness of the computing system.

In an example of a read operation, the post-slice de-manipulator 89receives at least a read threshold number of EC data slices and performsthe inverse function of the post-slice manipulator 81 to produce aplurality of encoded slices. The de-slicer 87 de-slices the encodedslices to produce an encoded data segment 94. The decoder 85 performsthe inverse function of the encoder 77 to recapture the data segment90-92. The pre-slice de-manipulator 83 performs the inverse function ofthe pre-slice manipulator 75 to recapture the data segment 90-92.

FIG. 5 is a diagram of an example of slicing an encoded data segment 94by the slicer 79. In this example, the encoded data segment 94 includesthirty-two bits, bytes, data words, etc., but may include more or lessbits, bytes, data words, etc. The slicer 79 disperses the bits of theencoded data segment 94 across the EC data slices in a pattern as shown.As such, each EC data slice does not include consecutive bits, bytes,data words, etc. of the data segment 94 reducing the impact ofconsecutive bit, byte, data word, etc. failures on data recovery. Forexample, if EC data slice 2 (which includes bits 1, 5, 9, 13, 17, 25,and 29) is unavailable (e.g., lost, inaccessible, or corrupted), thedata segment can be reconstructed from the other EC data slices (e.g.,1, 3 and 4 for a read threshold of 3 and a width of 4).

FIG. 6 is another schematic block diagram of an embodiment of acomputing system that includes a sending dispersed storage (DS)processing 102, a network 24, a dispersed storage network (DSN) memory22, a receiving DS processing 104, and a plurality of user devices 1-N.The computing system functions include transferring data 106 as encodeddata from the sending DS processing 102 to the receiving DS processing104 and producing reproduced data 108 based on received encoded data.The sending DS processing 102 transforms the data 106 into the encodeddata that includes two or more of a slice set 110, a zero informationgain (ZIG) slice set 114 (e.g., partial encoded data slices), a storedZIG slice set 122, and a stored slice set 118. The slice set 110includes less than a decode threshold number of encoded data slicescorresponding to the data 106. The slice set 110 is sent to thereceiving DS processing 104. The ZIG slice set 114 includes less than adecode threshold number of ZIG partials (e.g., recovery information)corresponding to at least one encoded data slice of the data 106. TheZIG slice set is sent to the receiving DS processing 104. The storedslice set 118 includes less than a decode threshold number of encodeddata slices corresponding to the data 106. The stored slice set 118 isstored in a first memory (e.g., a local memory, the DSN memory 22, oneor more DS units). The stored ZIG slice set 122 includes less than adecode threshold number of ZIG slices corresponding to at least oneencoded data slice of the data 106. The stored ZIG slice set 122 isstored in a second memory (e.g., a local memory, the DSN memory 22, oneor more DS units, and in at least one of the plurality of user devices1-N).

The sending DS processing 102 transforms the data 106 utilizing adispersed storage error coding function to produce one or more of theslice set 110, the ZIG slice set 114, the stored ZIG slice set 122, andthe stored slice set 118 in accordance with an encoding scheme. Theencoding scheme includes one or more of a number of encoded data slicesto encode indicator, a number of ZIG slices to encode indicator, one ormore encoded data slice identifiers (IDs), one or more ZIG slice IDs, apillar width n, a decode threshold k, an encoding matrix, a pillar indexthat identifies a ZIG slice association, a pillar participant list(e.g., other pillars associated with a subsequent decoding of a decodethreshold number of ZIG slices to reproduce an encoded data slice), anencryption key, one or more shared secrets, and one or more obfuscationvalues.

In an example of operation, the sending DS processing 102 dispersedstorage error encodes the data 106 in accordance with the encodingscheme to produce less than a decode threshold number of encoded dataslices of a set of encoded data slices for inclusion in at least one ofthe slice set 110 and the stored slice set 118. The sending DSprocessing 102 encodes at least one other encoded data slice of the setof encoded data slices in accordance with the encoding scheme to produceless than a decode threshold number of ZIG slices, hereafter referred toas ZIG partials or partials, for inclusion in at least one of the ZIGslice set 114 and the stored ZIG slice set 122.

The sending DS processing 102 may combine two or more partial sets tocreate a new partial set for inclusion as at least one of the ZIG sliceset 114 and/or the stored ZIG slice set 122. For example, the sending DSprocessing 102 utilizes an exclusive OR (XOR) logical function tocombine a first partial set and a second partial set to produce acombined partial set. The sending DS processing 102 may obfuscate thepartial set (e.g., combined or not) to produce an obfuscated partial setprior to sending or storing the associated partial set. The obfuscationmay include one or more of utilizing the XOR logical function, masking,encrypting, appending a constant, and performing a deterministicfunction. For example, the sending DS processing 102 obfuscates acombined partial set by utilizing the XOR logical function on thecombined partial set with an obfuscation value. The obfuscation valuemay be obtained by at least one of retrieving, performing a lookup,receiving, and utilizing a shared secret value. The shared secret valueis shared between the sending DS processing 102 and the receiving DSprocessing 104.

The sending DS processing 102 sends the slice set 110 and the ZIG sliceset 114 via network 24 to the receiving DS processing 104 in accordancewith the encoding scheme and/or a partial distribution scheme. Thepartial distribution scheme includes at least one of a partial setidentifier (ID), a transmission destination ID associated with a partialset ID, a storage destination ID associated with a partial set ID, anumber of partial sets to distribute, and a number of partial sets tostore. Alternatively, or in addition to, the sending DS processingfacilitates storing at least one of the stored ZIG slice set 122 and thestored slice set 118 in the DSN memory 22 in accordance with theencoding scheme and/or the partial distribution scheme. Alternatively,or in addition to, the sending DS processing 102 facilitates storing thestored ZIG slice set 122 in one or more user devices of the plurality ofuser devices 1-N in accordance with the encoding scheme and/or thepartial distribution scheme.

The receiving DS processing 104 receives one or more of a received sliceset 112 and a received ZIG slice set 116 from the sending DS processing102 via the network 24 when the sending DS processing 102 sends theslice set 110 and the ZIG slice set 114 corresponding to the receivedslice set 112 and the received ZIG slice set 116. The receiving DSprocessing 104 retrieves one or more of a retrieved ZIG slice set 124and a retrieved slice set 120 from the DSN memory 22 when insufficientencoded data is received directly from the sending DS processing 102(e.g., producing reproduced data from the received slice set 112 and thereceived ZIG slice set 116 is not possible). Alternatively, or inaddition to, the receiving DS processing 104 retrieves the retrieved ZIGslice set 124 from one or more user devices on the plurality of userdevices 1-N. The receiving DS processing 104 transforms one more encodeddata slices of one or more slice sets into at least one set of generatedpartials. The receiving DS processing 104 transforms at least onepartial of one or more of the received partial sets and the at least oneset of generated partials into at least one recovered encoded dataslice. The receiving DS processing 104 decodes the at least onerecovered encoded data slice and the received slice set 112 to producethe reproduced data 108. The method of operation of the sending DSprocessing 102 and the receiving DS processing 104 to transfer data isdiscussed in greater detail with reference to FIGS. 7A-13.

FIG. 7A is a diagram illustrating an example of transforming data 106into encoded data. Data 106 is dispersed storage error encoded toproduce at least a decode threshold number of slices that includesencoded data slices 1, 2, and 4 when a pillar width is 5, a decodethreshold is 3, and an encoding scheme indicates to encode slices 1, 2,and 4. Next, a partial p (3,4) is generated for slice 3 based on slice 4when the encoding scheme indicates to utilize slice 4 to generate apartial for slice 3. The partial p (3,4) is obfuscated to produce anobfuscated partial op (3,4). The obfuscated partial op (3,4) is sent asa less than a decode threshold number of obfuscated partials to at leastone receiving entity. Encoded data slices 1 and 2 are sent as less thana decode threshold number of encoded data slices to at least onereceiving entity.

FIG. 7B is a diagram illustrating another example of transforming data106 into encoded data. Data 106 is dispersed storage error encoded toproduce at least a decode threshold number of slices that includesencoded data slices 1, 4, and 5 when a pillar width is 5, a decodethreshold is 3, and an encoding scheme indicates to encode slices 1, 4,and 5. Next, partials p (2,4) and p (3,4) are generated for slices 2 and3 based on slice 4 when the encoding scheme indicates to utilize slice 4to generate partials for slices 2 and 3. Next, partials p (2,5) and p(3,5) are generated for slices 2 and 3 based on slice 5 when theencoding scheme indicates to utilize slice 5 to generate partials forslices 2 and 3.

Partials p (2,4) and p (2,5) are combined utilizing an exclusive OR(XOR) logical function to produce a combined partial p (2,4/5) when theencoding scheme indicates to combine partials p (2,4) and p (2,5)utilizing the XOR logical function. Partials p (3,4) and p (3,5) arecombined utilizing the XOR logical function to produce a combinedpartial p (3,4/5) when the encoding scheme indicates to combine partialsp (3,4) and p (3,5) utilizing the XOR logical function.

The combined partial p (2,4/5) is obfuscated to produce an obfuscatedpartial op (2,4/5). The combined partial p (3,4/5) is obfuscated toproduce an obfuscated partial op (3,4/5). The obfuscated partials op(2,4/5) and op (3,4/5) are sent as to send partials of less than adecode threshold number of obfuscated partials to at least one receivingentity. Encoded data slice 1, but not encoded data slices 4 and 5, issent as less than a decode threshold number of encoded data slices to atleast one receiving entity.

FIG. 7C is another schematic block diagram of an embodiment of acomputing system that includes a computing device 130, a receivingentity 132, an intermediary device 134, and a dispersed storage network(DSN) memory 22. The receiving entity 132 may be implemented as at leastone of a user device, a dispersed storage (DS) processing unit, a DSmanaging unit, and a DS unit. The intermediary device 134 may beimplemented as at least one of a user device, a dispersed storage (DS)processing unit, a DS managing unit, and a DS unit. The computing device130 may be implemented as at least one of a sending device, a userdevice, a dispersed storage (DS) processing unit, a DS managing unit,and a DS unit. For example, the computing device 130 is implementedutilizing a user device to send data, the intermediary device 134 isimplemented as a second user device affiliated with the computing device130, and the receiving entity 132 is implemented as a third user device.The computing device 130 includes a DS module 136. The DS module 136includes an encoding data module 138, an encode slice module 140, and anoutput module 142.

The encode data module 138 encodes data using a dispersed storage errorcoding function to produce a set of encoded data slices 144. The data106 can be recreated from a decode threshold number of encoded dataslices of the set of encoded data slices 144. The encode data module 138functions to encode the data 106 by a series of steps. In a first step,the encode module 138 divides the data into data blocks (e.g., datasegments). In a second step, the encode data module 138 encodes the datablocks using an encoding matrix of the dispersed storage error codingfunction to produce encoded data blocks. For example, the encode datamodule matrix multiplies a data segment by the encoding matrix toproduce a column of a slice matrix. In a third step, the encode datamodule 138 generates the set of encoded data slices 144 from the encodeddata blocks. For example, the encode data module 138 selects a column ofthe slice matrix to produce the set of encoded data slices 144.

The encode slice module 140 generates a zero information gain (ZIG)encoded data slice that represents a component of recovery informationof a first encoded data slice of the set of encoded data slices 144using a ZIG function and a second encoded data slice of the set ofencoded data slices 144. The encode slice module 140 functions togenerate the ZIG encoded data slice by a series of steps. In a firststep, the encode slice module 140 generates a decoding matrix for thefirst encoded data slice based on the encoding matrix of the dispersedstorage error coding function. The generating includes obtaining theencoding matrix utilized to generate the set of encoded data slices,reducing the encoding matrix to produce a square matrix that exclusivelyincludes rows associated with the first encoded data slice and a subsetof encoded data slices 148, and inverting the square matrix to producethe decoding matrix. In a second step, the encode slice module 140generates the ZIG encoded data slice 146 based on the decoding matrixand on the second encoded data slice. The generating includes encodingthe second encoded data slice using the decoding matrix to produce avector (e.g., matrix multiplying the decoding matrix by the secondencoded data slice to produce the vector) and matrix multiplying thevector by a row of the encoding matrix corresponding to the firstencoded data slice to produce the ZIG encoded data slice 146.

The output module 142 outputs the ZIG encoded data slice 146 and thesubset of encoded data slices 148 of the set of encoded data slices 146.The subset of encoded data slices 148 includes less than the decodethreshold number of encoded data slices and does not include the firstor the second encoded data slice. The outputting includes selecting thesubset of encoded data slices 148 based on one or more of a securityrequirement (e.g., requirement not to expose a slice generated from aunity matrix of an encoding matrix), a reliability requirement (e.g.,choose decode threshold number compatible with network error rate to thereceiving entity), a network bandwidth availability indicator, (e.g.,may minimize number of selected slices when bandwidth to the receivingentity is low), a DSN memory availability indicator, a dispersed storage(DS) unit availability indicator, a user device availability indicator,and a predetermination.

The output module 142 functions to output the ZIG encoded data slice 146and the subset of encoded data slices 148 by at least one of outputtingto the receiving entity 132 in support of a communication with thereceiving entity 132 (e.g., via a network), outputting to the DSN memory22 for storage therein (e.g., generate write slice requests, output therequests), and outputting to at least one intermediary device 134 (e.g.,in accordance with a predetermined list of user devices implemented asintermediary devices). The output module 142 further functions to outputby obfuscating the ZIG encoded data slice 146 utilizing an obfuscationfunction prior to outputting the ZIG encoded data slice 146. Theobfuscation function includes at least one of an exclusive OR functionwith a shared secret of the receiving entity 132 and an encryptingfunction utilizing at least one of a shared key and a public keyassociated with a public-private key pair of the receiving entity 132.

The output module 142 further functions to output ZIG functioninformation 150 regarding the encoding of the first encoded data slice.The ZIG function information 150 includes one or more of the encodingmatrix of the dispersed storage error coding function, an invertedsquare matrix based on the encoding matrix and corresponding to thefirst encoded data slice, and pillar identifiers (IDs) corresponding tothe subset of encoded data slices. The outputting includes one or moreof sending the ZIG information 150 to the receiving entity 132, sendingthe ZIG information 150 to the intermediary device 134, and facilitatingstorage of the ZIG information in the DSN memory 22.

The system may produce more than one ZIG encoded data slices 146 basedon more than one encoded data slice of the set of encoded data slices144. When producing more than one ZIG encoded data slice 146, the encodeslice module 140 generates a second ZIG encoded data slice 146 thatrepresents a component of recovery information of a third encoded dataslice of the set of encoded data slices 144 using the ZIG function andthe second encoded data slice or a fourth encoded data slice of the setof encoded data slices 144. The generating is based on the secondencoded data slice when at least two ZIG encoded data slices arerequired for a common encoded data slice (e.g., the second encoded dataslice). The encoding is based on the fourth encoded data slice whenanother ZIG encoded data slice is required for another encoded dataslice (e.g., the fourth encoded data slice). The output module 142outputs the ZIG encoded data slice 146, the second ZIG encoded dataslice of 46, and the subset of encoded data slices 148 of the set ofencoded data slices 144. When producing more than one ZIG encoded dataslice 146, the subset of encoded data slices 148 includes less than thedecode threshold number of encoded data slices and does not include thefirst, second, or third encoded data slice and, when the third encodeddata slice is encoded based on the fourth encoded data slice, the subsetof encoded data slices further does not include the fourth encoded dataslice.

The system may produce two or more ZIG encoded data slices 146 based ona common encoded data slice of the set of encoded data slices 144. Whenproducing two or more ZIG encoded data slices 146 based on a commonencoded data slice, the encode slice module 140 generates a second ZIGencoded data slice that represents a second component of the recoveryinformation of the first encoded data slice of the set of encoded dataslices using the ZIG function and a third encoded data slice of the setof encoded data slices. Next, the encode slice module 140 combines(e.g., exclusive OR) the second ZIG encoded data slice 146 with the ZIGencode data slice 146 to produce the ZIG encoded data slice 146. Next,the output module 142 outputs the ZIG encoded data slice 146 and thesubset of encoded data slices 148 of the set of encoded data slices 144.The subset of encoded data slices 148 includes less than the decodethreshold number of encoded data slices and does not include the first,second, or third encoded data slice when encoding the common encodeddata slice.

FIG. 7D is a flowchart illustrating an example of sending data. Themethod begins at step 152 were a processing module (e.g., of a dispersedstorage (DS) processing module) encodes data using a dispersed storageerror coding function to produce a set of encoded data slices. The datacan be recreated from a decode threshold number of encoded data slicesof the set of encoded data slices. The encoding the data includesdividing the data into data blocks, encoding the data blocks using anencoding matrix of the dispersed storage error coding function toproduce encoded data blocks, and generating the set of encoded dataslices from the encoded data blocks.

The method continues at step 154 where the processing module generates azero information gain (ZIG) encoded data slice that represents acomponent of recovery information of a first encoded data slice of theset of encoded data slices using a ZIG function and a second encodeddata slice of the set of encoded data slices. The generating the ZIGencoded data slice includes a sequence of steps. In a first step, theprocessor module generates a decoding matrix for the first encoded dataslice based on an encoding matrix of the dispersed storage error codingfunction. The generating includes obtaining the encoding matrix utilizedto generate the set of encoded data slices, reducing the encoding matrixto produce a square matrix that exclusively includes rows associatedwith the first encoded data slice and a subset of encoded data slices,and inverting the square matrix to produce the decoding matrix. In asecond step, processing module generates the ZIG encoded data slicebased on the decoding matrix and on the second encoded data slice. Thegenerating includes encoding the second encoded data slice using thedecoding matrix to produce a vector (e.g., matrix multiplying thedecoding matrix by the second encoded data slice to produce the vector)and matrix multiplying the vector by a row of the decoding matrixcorresponding to the first encoded data slice to produce the ZIG encodeddata slice.

In an example of generating the ZIG encoded data slice, the processingmodule generates a ZIG encoded data slice for encoded data slice 1 fromencoded data slice 2, denoted p(1,2), when a pillar index includes slice1, slice 2 is one of a decode threshold number of participant encodeddata slices, slice 1 is not one of the participant encoded data slices,and the participant encoded data slice pillars includes pillars 2-4. Forinstance, the processing module generates the ZIG encoded data slice p(1,2) in accordance with a function: partial (1,2)=(inverted squarematrix of an encoding matrix rows 2,3,4)*(data matrix with slice 2 inrow 1)*(row 1 of the encoding matrix), when a pillar width is 5, adecode threshold is 3.

The method continues at step 155 where the processing module outputs ZIGfunction information regarding the encoding of the first encoded dataslice. The outputting includes outputting to at least one of a receivingentity, an intermediary device, and a dispersed storage network (DSN)memory.

The system may produce more than one ZIG encoded data slice inaccordance with an encoding approach. The system may produce two or moreZIG encoded data slices in accordance with the encoding approach basedon a common encoded data slice of the set of encoded data slices. Theencoding approach includes one or more of a number of ZIG encoded dataslices to encode, a number of ZIG encoded data slices per common encodeddata slice to encode, a decode threshold number, the encoding matrix,and a pillar width number. The processing module may obtain the encodingapproach based on at least one of a lookup, and predetermination,receiving, and calculating based on one or more of a securityrequirement, a reliability requirement, and a performance requirement.The method branches to step 158 when producing more than one ZIG encodeddata slice. The method branches to step 162 when utilizing the commonencoded data slice. The method continues to step 156 when producing oneZIG encoded data slice.

When producing one ZIG encoded data slice, the method continues at step156 where the processing module outputs the ZIG encoded data slice andthe subset of encoded data slices of the set of encoded data slices. Thesubset of encoded data slices includes less than the decode thresholdnumber of encoded data slices and does not include the first or thesecond encoded data slice. The outputting includes selecting the subsetof encoded data slices is based on one or more of a security requirement(e.g., requirement not to expose a slice generated from a unity matrixof an encoding matrix), a reliability requirement (e.g., choose decodethreshold number compatible with network error rate to the receivingentity), a network bandwidth availability indicator, (e.g., may minimizenumber of selected slices when bandwidth to the receiving entity islow), a dispersed storage network (DSN) memory availability indicator, adispersed storage (DS) unit availability indicator, a user deviceavailability indicator, and a predetermination. The outputting furtherincludes obfuscating the ZIG encoded data slice utilizing an obfuscationfunction (e.g. exclusive OR), prior to outputting the ZIG encoded dataslice.

The outputting the ZIG encoded data slice and the subset of encoded dataslices includes at least one of a variety of approaches. In a firstapproach, the processing module outputs to a receiving entity in supportof a communication with the receiving entity. In a second approach, theprocessing module outputs to a dispersed storage network (DSN) memoryfor storage therein. For example, the processing module generates awrite slice request for the ZIG encoded data slice that includes the ZIGencoded data slice. For each encoded data slice of the subset of encodeddata slices, the processing module generates a write slice request thatincludes the encoded data slice of the subset of encoded data slices.Next, the processing module outputs the write slice request associatedwith the ZIG encoded data to the DSN memory. For each encoded data sliceof the subset of encoded data slices, the processing module outputs acorresponding write slice request to the DSN memory. In a thirdapproach, the processing module outputs to at least one intermediarydevice.

When producing more than one ZIG encoded data slice, the methodcontinues at step 158 where the processing module generates a second ZIGencoded data slice that represents a component of recovery informationof a third encoded data slice of the set of encoded data slices usingthe ZIG function and the second encoded data slice or a fourth encodeddata slice of the set of encoded data slices. The method continues atstep 160 where the processing module outputs the ZIG encoded data slice,the second ZIG encoded data slice, and the subset of encoded data slicesof the set of encoded data slices. The subset of encoded data slicesincludes less than the decode threshold number of encoded data slicesand does not include the first, second, or third encoded data slice and,when the third encoded data slice is encoded based on the fourth encodeddata slice, the subset of encoded data slices further does not includethe fourth encoded data slice.

When producing two or more ZIG encoded data slices utilizing the commonencoded data slice, the method continues at step 162 where theprocessing module generates a second ZIG encoded data slice thatrepresents a second component of the recovery information of the firstencoded data slice of the set of encoded data slices using the ZIGfunction and a third encoded data slice of the set of encoded dataslices. The method continues at step 164 where the processing modulecombines (e.g., exclusive OR) the second ZIG encoded data slice with theZIG encode data slice to produce the ZIG encoded data slice. The methodcontinues at step 166 where the processing module outputs the ZIGencoded data slice and the subset of encoded data slices of the set ofencoded data slices. The subset of encoded data slices includes lessthan the decode threshold number of encoded data slices and does notinclude the first, second, or third encoded data slice.

FIG. 8A is a diagram illustrating an example of transforming encodeddata into reproduced data 108. Encoded data slices 1 and 2 are receivedas a less than a decode threshold number of slices to produce receivedencoded data slices. Obfuscated partial op (3,4) is received as lessthan a decode threshold number of partials to produce received partials.Partial p (3,1) is generated from received encoded data slice 1 andpartial p (3,2) is generated from received encoded data slice 2.Received partial op (3,4) is de-obfuscated to produce received partial p(3,4). Generated partials p (3,1) and p (3,2) are combined with receivedpartial p (3,4) to produce recovered encoded data slice 3. Recoveredencoded data slice 3 is dispersed storage error decoded along withreceived encoded data slices 1 and 2 to produce reproduced data 108.

FIG. 8B is a diagram illustrating another example of transformingencoded data into reproduced data 108. Encoded data slice 1 is receivedas a less than a decode threshold number of slices to produce a receivedencoded data slice 1. Obfuscated partial op (2,4/5) is received as lessthan a decode threshold number of partials to produce a received partialop (2,4/5). Obfuscated partial op (3,4/5) is received as less than adecode threshold number of partials to produce a received partial op(3,4/5). Partials p (2,1) and p (3,1) are generated from receivedencoded data slice 1. Received partial op (2,4/5) is de-obfuscated toproduce received partial p (2,4/5). Received partial op (3,4/5) isde-obfuscated to produce received partial p (3,4/5). Generated partial p(2,1) is combined with received partial p (2,4/5) to produce recoveredencoded data slice 2. Generated partial p (3,1) is combined withreceived partial p (3,4/5) to produce recovered encoded data slice 3.Recovered encoded data slices 2 and 3 are dispersed storage errordecoded along with received encoded data slice 1 to produce reproduceddata 108.

FIG. 8C is another schematic block diagram of an embodiment of acomputing system that includes a computing device 170, a sending entity172, an intermediary device 134, and a dispersed storage network (DSN)memory 22. The sending entity 172 may be implemented as at least one ofa user device, a dispersed storage (DS) processing unit, a DS managingunit, and a DS unit. The intermediary device 134 may be implemented asat least one of a user device, a dispersed storage (DS) processing unit,a DS managing unit, and a DS unit. The computing device 170 may beimplemented as at least one of a receiving entity, a user device, adispersed storage (DS) processing unit, a DS managing unit, and a DSunit. For example, the sending entity 172 is implemented utilizing auser device to send data, the intermediary device 134 is implemented asa second user device affiliated with the computing device 170, and thecomputing device 170 is implemented as a third user device. Thecomputing device 170 includes a DS module 174. The DS module 174includes a receive module 176, a generate module 178, a recreate module180, and a decode module 182.

The receive module 176 receives a zero information gain (ZIG) encodeddata slice 146 and a subset of encoded data slices 148 of a set ofencoded data slices. Data 106 was encoded using a dispersed storageerror coding function to produce the set of encoded data slices. Data106 can be recreated from a decode threshold number of encoded dataslices of the set of encoded data slices. The subset of encoded dataslices 148 includes less than the decode threshold number of encodeddata slices and does not include a first or a second encoded data sliceof the set of encoded data slices. The ZIG encoded data slice 146represents a first component of recovery information of the firstencoded data slice 186 that is based on the second encoded data slice.The receive module 176 may obtain ZIG function information 150 regardingthe generating of the ZIG encoded data slice 146. The receive module 176receives the ZIG encoded data slice 146, the subset of encoded dataslices 148, and the ZIG function information 150 from one or more of theintermediary device 134 (e.g., in response to a request), the sendingentity 172, and the DSN memory 22 (e.g., in response to a request).

The generate module 178 generates a set of ZIG encoded data slices 184using a ZIG function and corresponding ones of the subset of encodeddata slices 148. The set of ZIG encoded data slices 184 representsadditional components of the recovery information of the first encodeddata slice 186. The generate module 178 functions to generate one of theset of ZIG encoded data slices 184 by generating a decoding matrix forthe first encoded data slice 186 based on an encoding matrix of thedispersed storage error coding function and generating the one of theset of ZIG encoded data slices 184 based on the decoding matrix and on acorresponding one of the subset of encoded data slices 148. The generatemodule 178 functions to generate the decoding matrix by reducing theencoding matrix to produce a square matrix based on the first encodeddata slice 186 and the subset of encoded data slices 148 (e.g., squarematrix includes rows associated with the first encoded data slice 186and the subset of encoded data slices) and inverting the square matrixto produce the decoding matrix.

The generate module 178 functions to generate the one of the set of ZIGencoded data slices 184 based on the decoding matrix by encoding thecorresponding one of the subset of encoded data slices 148 using thedecoding matrix to produce a vector (e.g., matrix multiplying thedecoding matrix by the corresponding one of the subset of encoded dataslices 148 to produce the vector) and encoding the vector by a row ofthe decoding matrix corresponding to the first encoded data slice 186 toproduce the one of the set of ZIG encoded data slices 184 (e.g., matrixmultiplying the vector by a row of the decoding matrix corresponding tothe first encoded data slice 186 to produce the one of the set of ZIGencoded data slices 184).

The recreate module 180 recreates the first encoded data slice 186 fromthe ZIG encoded data slice 146 and the set of ZIG encoded data slices184. Prior to recreating the first encoded data slice 186, the recreatemodule 180 functions to de-obfuscate the ZIG encoded data slice 146utilizing an obfuscation function when the ZIG encoded data slice 146was obfuscated. For example, the recreate module 180 performs anexclusive OR function on the ZIG encoded data slice 146 with a sharedsecret to de-obfuscate the ZIG encoded data slice 146. The shared secretincludes at least one of a private key, a secret value shared with thesending entity 172, a shared secret value of the ZIG information 150.

The recreate module 180 recreates the first encoded data slice 186 fromthe ZIG encoded data slice 146 and the set of ZIG encoded data slices184 by one of a variety of approaches. In a first approach, the recreatemodule 180 exclusive ORs the ZIG encoded data slice 146 and the set ofZIG encoded data slices 184 to produce the first encoded data slice 186.In a second approach, the recreate module 180 rebuilds the first encodeddata slice 186 based on the ZIG encoded data slice 146 and the set ofZIG encoded data slices 184 in accordance with a dispersed storage errorcoding function.

The decode module 182 decodes the subset of encoded data slices 148 andthe first encoded data slice 186 using the dispersed storage errorcoding function to reproduce the data 106. The decode module 182 decodesthe subset of encoded data slices 148 and the first encoded data slice186 by a series of steps. In a first step, the decode module 182generates a received slice matrix from the first encoded data slice 186and the subset of encoded data slices 148 (e.g., the received slicematrix includes decode threshold number of rows). In a second step, thedecode module 182 generates a data matrix based on the received slicematrix and a decoding matrix. The generating includes matrix multiplyingthe received slice matrix by the decoding matrix to produce the datamatrix. In a third step, the decode module 182 creates the data 106 fromthe data matrix. The creating includes aggregating the data matrix toform the data 106. The decode module 182 may generate the decodingmatrix by a series of steps. In a first step, the decode module 182obtains an encoding matrix utilized to generate the set of encoded dataslices (e.g., receives ZIG information 150). In a second step, thedecode module 182 reduces the encoding matrix based on rows associatedwith the subset of encoded data slices 148 and the first encoded dataslice 186 to produce a square matrix. In a third step, the decode module182 converts the square matrix to produce the decoding matrix.

FIG. 8D is a flowchart illustrating an example of receiving data. Themethod begins at step 190 where a processing module (e.g., of areceiving entity) receives a zero information gain (ZIG) encoded dataslice and a subset of encoded data slices of a set of encoded dataslices. Data was encoded using a dispersed storage error coding functionto produce the set of encoded data slices. The data can be recreatedfrom a decode threshold number of encoded data slices of the set ofencoded data slices. The subset of encoded data slices includes lessthan the decode threshold number of encoded data slices and does notinclude a first or a second encoded data slice of the set of encodeddata slices. The ZIG encoded data slices represents a first component ofrecovery information of the first encoded data slice that is based onthe second encoded data slice.

The method continues at step 192 where the processing module obtains ZIGfunction information regarding the generating of the ZIG encoded dataslice. The obtaining includes at least one of receiving the ZIG functioninformation with the ZIG encoded data slice, retrieving the ZIG functioninformation from a dispersed storage network (DSN) memory, and receivingthe ZIG function information from an intermediary device in response toa request.

The method continues at step 194 where the processing module generates aset of ZIG encoded data slices using a ZIG function and correspondingones of the subset of encoded data slices. The set of ZIG encoded dataslices represents additional components of the recovery information ofthe first encoded data slice. The generating one of the set of ZIGencoded data slices includes generating a decoding matrix for the firstencoded data slice based on an encoding matrix of the dispersed storageerror coding function and generating the one of the set of ZIG encodeddata slices based on the decoding matrix and on a corresponding one ofthe subset of encoded data slices. The generating the decoding matrixincludes reducing the encoding matrix to produce a square matrix basedon the first encoded data slice and the subset of encoded data slices(e.g., exclusively includes rows associated with the first encoded dataslice and the subset of encoded data slices) and inverting the squarematrix to produce the decoding matrix.

The generating the one of the set of ZIG encoded data slices based onthe decoding matrix includes encoding the corresponding one of thesubset of encoded data slices using the decoding matrix to produce avector (e.g., matrix multiplying the decoding matrix by thecorresponding one of the subset of encoded data slices to produce thevector) and encoding the vector by a row of the decoding matrixcorresponding to the first encoded data slice to produce the one of theset of ZIG encoded data slices. The encoding includes matrix multiplyingthe vector by a row of the decoding matrix corresponding to the firstencoded data slice to produce the one of the set of ZIG encoded dataslices.

Prior to recreating the first encoded data slice, the method continuesat step 196 where the processing module de-obfuscates the ZIG encodeddata slice utilizing an obfuscation function when the first encoded dataslice was obfuscated. For example, the processing module will performsan exclusive OR (XOR) function on the ZIG encoded data slice with ashared secret to de-obfuscate the ZIG encoded data slice. The sharedsecret includes at least one of a private key, a secret value sharedwith a sending entity, a shared secret value of the ZIG information. Asanother example, the processing module de-obfuscates the ZIG encodeddata slice by utilizing the XOR function on the ZIG encoded data sliceand with a corresponding obfuscation value (e.g., a pillar number).

The method continues at step 198 where the processing module recreatesthe first encoded data slice from the ZIG encoded data slice and the setof ZIG encoded data slices. The recreating the first encoded data slicefrom the ZIG encoded data slice and the set of ZIG encoded data slicesincludes one of a variety of approaches. A first approach includesexclusive ORing the ZIG encoded data slice and the set of ZIG encodeddata slices to produce the first encoded data slice. A second approachincludes rebuilding the first encoded data slice based on the ZIGencoded data slice and the set of ZIG encoded data slices in accordancewith a dispersed storage error coding function.

The method continues at step 200 and processing module decodes thesubset of encoded data slices and the first encoded data slice using thedispersed storage error coding function to reproduce the data. Thedecoding the subset of encoded data slices and the first encoded dataslice includes a series of steps. A first step includes generating areceived slice matrix from first encoded data slice and the subset ofencoded data slices (e.g., the received slice matrix includes decodethreshold number of rows). A second step includes generating a datamatrix based on the received slice matrix and a decoding matrix. Thegenerating includes matrix multiplying the received slice matrix by thedecoding matrix to produce the data matrix. A third step includescreating the data from the data matrix. The creating includesaggregating the data matrix to form the data. The processing module mayproduce the decoding matrix by a series of steps. A first step includesobtaining an encoding matrix utilized to generate the set of encodeddata slices. A second step includes reducing the encoding matrix basedon rows associated with the subset of encoded data slices and the firstencoded data slice to produce a square matrix. A third step includesinverting the square matrix to produce the decoding matrix.

FIG. 9A is a diagram illustrating an example of generation of a set ofzero information gain (ZIG) encoded data slices to facilitate sending anencoded data slice (e.g., slice 1) from a sending entity to a receivingentity. The sending includes a series of steps. A first step includesdetermining whether to send an encoded data slice of a set of encodeddata slices in accordance with a ZIG format. Data (e.g., a data segment)is encoded (e.g., by the sending entity) using a dispersed storage errorcoding function to produce the set of encoded data slices. The data canbe recreated (e.g., by the receiving entity) from a decode thresholdnumber of encoded data slices of the set of encoded data slices. Forexample, sending entity receives an error message from the receivingentity indicating that encoded data slice 1 is missing with regards to aprevious slice transfer. The sending entity determines to send encodeddata slice 1 in accordance with the ZIG format based on the errormessage.

When sending the encoded data slice in accordance with the ZIG format, asecond step includes selecting a partial encoding threshold number ofencoded data slices of the set of encoded data slices. The partialencoding threshold number may be substantially the same as the decodethreshold number of the dispersed storage error coding function. Theselection results in the partial encoding threshold number of encodeddata slices such that the partial encoding threshold number of encodeddata slices does not include the encoded data slice. For example, thesending entity selects encoded data slices 2-4 of the set of encodeddata slices 1-5.

A third step includes generating a set of ZIG encoded data slices basedon a ZIG function and the partial encoding threshold number of encodeddata slices. The set of ZIG encoded data slices represents recoveryinformation of the encoded data slice (e.g., the receiving entityre-creates encoded data slice 1 based on the set of ZIG encoded dataslices. For example, the sending entity generates the set of ZIG encodeddata slices by generating partial p (1,2) (e.g., a ZIG encoded dataslice that represents a portion of recovery information of encoded dataslice 1) based on encoded data slice 2 for missing encoded data slice 1,generates partial p (1,3) based on encoded data slice 3 for missingencoded data slice 1, and generates partial p (1,4) based on encodeddata slice 4 for missing encoded data slice 1. The generating mayinclude obfuscating one or more of the ZIG encoded data slices. Forexample, the sending entity obfuscates partials p (1,2), p (1,3), and p(1,4) prior to outputting to produce obfuscated partials op (1,2), op(1,3), and op (1,4).

A fourth step includes outputting the set of ZIG encoded data slices tothe receiving entity. The outputting may include utilizing one or morecommunication paths and/or one or more intermediary devices thatincludes temporary storage. For example, the sending entity outputsobfuscated partials op (1,2), op (1,3), and op (1,4) to the receivingentity. The receiving entity receives the partial encoding thresholdnumber of obfuscated partials op (1,2), op (1,3), and op (1,4). Thereceiving entity de-obfuscates obfuscated partials op (1,2), op (1,3),and op (1,4) to reproduce partials p (1,2), p (1,3), and p (1,4). Thereceiving entity combines partials p (1,2), p (1,3), and p (1,4) toreproduce missing encoded data slice 1. For instance, the receivingentity performs the exclusive OR function on partials p (1,2), p (1,3),and p (1,4) to reproduce missing encoded data slice 1.

FIG. 9B is a diagram illustrating another example of generation of a setof zero information gain (ZIG) encoded data slices to facilitate sendingan encoded data slice (e.g., slice 1) from a sending entity to areceiving entity. The sending includes a series of steps. A first stepincludes determining whether to send an encoded data slice of a set ofencoded data slices in accordance with a ZIG format. Data (e.g., a datasegment) is encoded (e.g., by the sending entity) using a dispersedstorage error coding function to produce the set of encoded data slices.The data can be recreated (e.g., by the receiving entity) from a decodethreshold number of encoded data slices of the set of encoded dataslices. For example, sending entity receives a security message from amanaging entity indicating that encoded data slice 1 shall betransferred utilizing the ZIG format. The sending entity determines tosend encoded data slice 1 in accordance with the ZIG format based on thesecurity message.

When sending the encoded data slice in accordance with the ZIG format, asecond step includes selecting a partial encoding threshold number ofencoded data slices of the set of encoded data slices. The partialencoding threshold number may be substantially the same as the decodethreshold number of the dispersed storage error coding function. Theselection results in the partial encoding threshold number of encodeddata slices such that the partial encoding threshold number of encodeddata slices does not include the encoded data slice. For example, thesending entity selects encoded data slices 2-4 of the set of encodeddata slices 1-5.

A third step includes generating a set of ZIG encoded data slices basedon a ZIG function and the partial encoding threshold number of encodeddata slices. The set of ZIG encoded data slices represents recoveryinformation of the encoded data slice (e.g., the receiving entityre-creates encoded data slice 1 based on the set of ZIG encoded dataslices. For example, the sending entity generates the set of ZIG encodeddata slices by generating partial p (1,2) (e.g., a ZIG encoded dataslice that represents a portion of recovery information of encoded dataslice 1) based on encoded data slice 2 for missing encoded data slice 1,generates partial p (1,3) based on encoded data slice 3 for missingencoded data slice 1, and generates partial p (1,4) based on encodeddata slice 4 for missing encoded data slice 1.

A fourth step includes combining two or more ZIG encoded data slices ofthe set of ZIG encoded data slices. For example, the sending entitycombines partial p(1,3) with partial p(1,4) utilizing an exclusive ORfunction to produce partial p(1,3/4). The combining may includeobfuscating one or more of the ZIG encoded data slices prior tooutputting. For example, the sending entity obfuscates partials p (1,2)and p (1,3/4) prior to outputting to produce obfuscated partials op(1,2) and op (1,3/4).

A fifth step includes outputting the set of ZIG encoded data slices tothe receiving entity. The outputting includes utilizing two or morecommunication paths and/or intermediary devices that includes temporarystorage. Utilizing two or more paths may provide one or more of anetwork bandwidth utilization improvement and a security improvement tothe system. For example, the sending entity outputs obfuscated partialop (1,2) via a first communication path to the receiving entity andoutputs obfuscated partial op (1,3/4) via a second communication path.The receiving entity receives obfuscated partials op (1,2) and op(1,3/4). The receiving entity de-obfuscates obfuscated partials op (1,2)and op (1,3/4) to reproduce partials p (1,2) and p (1,3/4). Thereceiving entity combines partials p (1,2) and p (1,3/4) to reproducemissing encoded data slice 1. For instance, the receiving entityperforms the exclusive OR function on partials p (1,2) and p (1,3/4) toreproduce missing encoded data slice 1.

FIG. 9C is another schematic block diagram of an embodiment of acomputing system that includes a computing device 210, a receivingentity 132, an intermediary device 134, and a dispersed storage network(DSN) memory 22. The receiving entity 132 may be implemented as at leastone of a user device, a dispersed storage (DS) processing unit, a DSmanaging unit, and a DS unit. The intermediary device 134 may beimplemented as at least one of a user device, a dispersed storage (DS)processing unit, a DS managing unit, and a DS unit. The computing device210 may be implemented as at least one of a sending device, a userdevice, a dispersed storage (DS) processing unit, a DS managing unit,and a DS unit. For example, the computing device 210 is implementedutilizing a user device to send data, the intermediary device 134 isimplemented as a second user device affiliated with the computing device210, and the receiving entity 132 is implemented as a third user device.The computing device 210 includes a DS module 212. The DS module 212includes a send determination module 214, a generate module 216, and anoutput module 218.

The DS module 212 obtains a set of encoded data slices 144. Theobtaining includes at least one of receiving the set of encoded dataslices 144, retrieving the set of encoded data slices 144, andgenerating the set of encoded data slices 144. For example, the DSmodule 212 encodes data 106 using a dispersed storage error codingfunction to produce the set of encoded data slices 144 when theobtaining includes generating the set of encoded data slices 144. Thedata 106 can be recreated from a decode threshold number of encoded dataslices of the set of encoded data slices 144.

The send determination module 214 determines whether to send an encodeddata slice of set of encoded data slices 144 in accordance with a zeroinformation gain (ZIG) format. The send determination module 214functions to determine whether to send the encoded data slice in the ZIGformat by at least one of a variety of approaches. A first approachincludes receiving an error message with regards to a previoustransmission of the encoded data slice. A second approach includesdetermining that the encoded data slice is of a first priority type(e.g., a security risk if the slice were to be transmitted as is). Athird approach includes receiving a request for transmission of theencoded data slice. A fourth approach includes determining that a slicename associated with the encoded data slice is on a list (e.g., slicenames not to be sent directly).

When the encoded data slice is to be sent in accordance with the ZIGformat, the generate module 216 selects a partial encoding thresholdnumber of encoded data slices of the set of encoded data slices 144. Thepartial encoding threshold number of encoded data slices does notinclude the encoded data slice. The generate module 216 functions toselect the partial encoding threshold number of encoded data slices byselecting a subset of encoded data slices of the set of encoded dataslices 144 to fulfill the decode threshold number of encoded data slicesrequirement for recreating the data. The selecting the subset of encodeddata slices includes at least one of a variety of approaches. A firstapproach includes selecting at least one of the subset of encoded dataslices to include encoded error code blocks (e.g., may choose an errorcoded slice rather than a data slice when a unity matrix is utilizedwithin an encoding matrix used to generate the set of encoded dataslices). A second approach includes selecting at least one other of thesubset of encoded data slices to include encoded data blocks (e.g.,indicator from a receiving entity indicates that a corresponding ZIGencoded data slice already exists).

The generate module 216 generates a set of ZIG encoded data slices 220based on a ZIG function and the partial encoding threshold number ofencoded data slices. The set of ZIG encoded data slices 220 representsrecovery information of the encoded data slice. The generate module 216generates a ZIG encoded data slice of the set of ZIG encoded data slices220 by generating a decoding matrix for the encoded data slice based onan encoding matrix of the dispersed storage error coding function andgenerating the ZIG encoded data slice based on the decoding matrix andon a first encoded data slice of the partial encoding threshold numberof encoded data slices.

The generate module 216 generates the decoding matrix by reducing theencoding matrix to produce a square matrix based on the partial encodingthreshold number of encoded data slices and inverting the square matrixto produce the decoding matrix. The generate module 216 generates theZIG encoded data slice based on the decoding matrix and on the encodeddata slice by a series of steps. A first step includes encoding thefirst encoded data slice using the decoding matrix to produce a vector.The encoding includes matrix multiplying the decoding matrix by thefirst encoded data slice to produce the vector. A second step includesencoding the vector by a row of the decoding matrix corresponding to theencoded data slice to produce the ZIG encoded data slice. The encodingincludes multiplying the vector by a row of the decoding matrixcorresponding to the encoded data slice to produce the ZIG encoded dataslice.

Alternatively, the generate module 216 generates the ZIG encoded dataslice of the set of ZIG encoded data slices by a series of alternativesteps. A first alternate step includes generating the decoding matrixfor the encoded data slice based on the encoding matrix of the dispersedstorage error coding function. A second alternative step includesgenerating a first initial ZIG encoded data slice based on the decodingmatrix and on a first encoded data slice of the partial encodingthreshold number of encoded data slices. A third alternative stepincludes generating a second initial ZIG encoded data slice based on thedecoding matrix and on a second encoded data slice of the partialencoding threshold number of encoded data slices. A fourth alternativestep includes combining (e.g., exclusive OR) the first and secondinitial ZIG encoded data slices to produce the ZIG encoded data slice.

The output module 218 outputs the set of ZIG encoded data slices 220.The output module 218 outputs the set of ZIG encoded data slices 220 byat least one of a variety of approaches. A first approach includesoutputting a first one of the set of ZIG encoded data slices 220 on afirst path and outputting a second one of the set of ZIG encoded dataslices 220 on a second path. A second approach includes outputting to areceiving entity in support of a communication with the receiving entity(e.g., via a network). A third approach includes outputting to adispersed storage network (DSN) memory for storage therein (e.g.,generate write slice requests, output the requests). A fourth approachincludes outputting to at least one intermediary device (e.g., aretrieving entity has a predetermined list of devices including the atleast one intermediary device). Prior to outputting the set of ZIGencoded data slices 220, the output module 218 may output by obfuscatingat least one ZIG encoded data slice of the set of ZIG encoded dataslices 220 utilizing an obfuscation function (e.g., exclusive OR with ashared secret of the receiving entity, encrypt utilizing a key known tothe receiving entity).

FIG. 9D is a flowchart illustrating an example generating a set of zeroinformation gain (ZIG) encoded data slices. The method begins at step230 were a processing module (e.g., of a sending entity) determineswhether to send an encoded data slice of a set of encoded data slices inaccordance with a zero information gain (ZIG) format. Data is encodedusing a dispersed storage error coding function to produce the set ofencoded data slices. The data can be recreated from a decode thresholdnumber of encoded data slices of the set of encoded data slices. Thedetermining whether to send the encoded data slice in the ZIG formatincludes at least one of a variety of approaches. A first approachincludes receiving an error message with regards to a previoustransmission of the encoded data slice. A second approach includesdetermining that the encoded data slice is of a first priority type;(e.g., high-priority). A third approach includes receiving a request fortransmission of the encoded data slice (e.g., utilizing the ZIG format).A fourth approach includes determining that a slice name associated withthe encoded data slice is on a list. (e.g., a list of slice names slatedfor utilizing the ZIG format).

When the encoded data slice is to be sent in accordance with the ZIGformat, the method continues at step 232 where the processing moduleselects a partial encoding threshold number of encoded data slices ofthe set of encoded data slices. The partial encoding threshold number ofencoded data slices does not include the encoded data slice. Theselecting the partial encoding threshold number of encoded data slicesincludes a series of steps. A first step includes selecting a subset ofencoded data slices of the set of encoded data slices to fulfill thedecode threshold number of encoded data slices requirement forrecreating the data. The selecting the subset of encoded data slicesincludes at least one of selecting at least one of the subset of encodeddata slices to include encoded error code blocks (e.g., may choose anerror coded slice rather than a data slice) and selecting at least oneother of the subset of encoded data slices to include encoded datablocks (e.g., an indicator from a receiving entity indicates that acorresponding ZIG encoded data slice already exists).

The method continues at step 234 where the processing module generates aset of ZIG encoded data slices based on a ZIG function and the partialencoding threshold number of encoded data slices. The set of ZIG encodeddata slices represents recovery information of the encoded data slice.The generating the ZIG encoded data slice of the set of ZIG encoded dataslices includes generating a decoding matrix for the encoded data slicebased on an encoding matrix of the dispersed storage error codingfunction and generating the ZIG encoded data slice based on the decodingmatrix and on a first encoded data slice of the partial encodingthreshold number of encoded data slices. The generating the decodingmatrix includes reducing the encoding matrix to produce a square matrixbased on the partial encoding threshold number of encoded data slicesand inverting the square matrix to produce the decoding matrix.

The generating the ZIG encoded data slice based on the decoding matrixand on the encoded data slice includes a series of steps. A first stepincludes encoding the first encoded data slice using the decoding matrixto produce a vector. The encoding includes matrix multiplying thedecoding matrix by the first encoded data slice to produce the vector. Asecond step includes encoding the vector by a row of the decoding matrixcorresponding to the encoded data slice to produce the ZIG encoded dataslice. The encoding includes multiplying the vector by a row of thedecoding matrix corresponding to the encoded data slice to produce theZIG encoded data slice.

Alternatively, when utilizing two or more communication paths and/orintermediary devices that include storage, the generating the ZIGencoded data slice of the set of ZIG encoded data slices includes analternate series of steps. A first alternate step includes generating adecoding matrix for the encoded data slice based on an encoding matrixof the dispersed storage error coding function. A second alternate stepincludes generating a first initial ZIG encoded data slice based on thedecoding matrix and on a first encoded data slice of the partialencoding threshold number of encoded data slices. A third alternate stepincludes generating a second initial ZIG encoded data slice based on thedecoding matrix and on a second encoded data slice of the partialencoding threshold number of encoded data slices. A fourth alternatestep includes combining (e.g., exclusive OR) the first and secondinitial ZIG encoded data slices to produce the ZIG encoded data slice.

Prior to outputting the set of ZIG encoded data slices, the methodcontinues at step 236 where the processing module obfuscates at leastone ZIG encoded data slice of the set of ZIG encoded data slicesutilizing an obfuscation function. The method continues at step 238where the processing module outputs the set of ZIG encoded data slices.The outputting the set of ZIG encoded data slices includes at least oneof a series of steps. A first step includes outputting a first one ofthe set of ZIG encoded data slices on a first path and outputting asecond one of the set of ZIG encoded data slices on a second path. Asecond step includes outputting to a receiving entity in support of acommunication with the receiving entity (e.g., via a network). A thirdstep includes outputting to a dispersed storage network (DSN) memory forstorage therein (e.g., generate write slice requests, output therequests). A fourth step includes outputting to at least oneintermediary device (e.g., retrieving entity has a predetermined list ofuser devices to retrieve).

FIG. 10 is a flowchart illustrating an example of storing encoded data.The method begins at step 240 where a processing module (e.g., of asending dispersed storage (DS) processing, of a user device, of a DSprocessing unit) obtains an encoding scheme. The obtaining includes atleast one of receiving, retrieving, and determining. The encoding schemeincludes one or more of a decode threshold number, a number of encodeddata slices to send, a number of zero information gain encoded dataslices to send, an obfuscation of slices indicator, a securityrequirement, a performance requirement, and a reliability requirement.The method continues at step 242 where the processing module encodesdata in accordance with the encoding scheme to produce at least a decodethreshold number of encoded data slices of a set of encoded data slices.The method continues at step 244 where the processing module generatesat least one partial slice corresponding to another encoded data sliceof the set of encoded data slices from at least one of the least adecode threshold number of encoded data slices in accordance with theencoding scheme. The method continues at step 246 where the processingmodule obfuscates the at least one partial slice to produce at least oneobfuscated partial slice.

The method continues at step 248 where the processing module determinesa partial distribution scheme. The determination may be based on one ormore of a goal, a security requirement, a reliability requirement, aperformance requirement, a receiving entity list, the data, the datatype of the data, a received message, the list, and a lookup. Forexample, the processing module determines the partial distributionscheme to include sending an obfuscated partial slice to each userdevice of a plurality of user devices for storage therein based on asecurity requirement to utilize trusted user devices. As anotherexample, the processing module determines the partial distributionscheme to include sending all obfuscated partial slices to a dispersedstorage network (DSN) memory for storage therein when a performancerequirement indicates to utilize the DSN memory for fast retrievals.

The method continues at step 250 where the processing module sends theat least one obfuscated partial slice to at least one receiving entityfor storage therein in accordance with the partial distribution scheme.The method continues at step 252 where the processing module sends eachof the at least a decode threshold number of encoded data slices exceptfor the at least one encoded data slice to a DSN memory for storagetherein.

FIG. 11 is a flowchart illustrating an example of retrieving encodeddata, which includes similar steps to FIG. 10. The method begins withstep 240 of FIG. 10 where a processing module (e.g., of a receivingdispersed storage (DS) processing, of a user device, of a DS processingunit) obtains an encoding scheme. The method continues at step 256 wherethe processing module retrieves less than a decode threshold number ofencoded data slices from a dispersed storage network (DSN) memory toproduce received encoded data slices. For example, a processing moduledetermines to retrieve the encoded data slices from a DSN memory basedon an indication of the encoding scheme to retrieve the encoded dataslices from the DSN memory. As another example, the processing modulereceives a message from a sending entity indicating to retrieve theencoded data slices from the DSN memory.

The method continues at step 258 where the processing module obtains apartial distribution scheme. The obtaining may be based on one or moreof a lookup, a predetermination, receiving the partial distributionscheme from a sending DS processing unit, retrieving from the DSNmemory, and determining the partial distribution scheme based on one ormore of a goal, a security requirement, a reliability requirement, aperformance requirement, a receiving entity list, the data, the datatype of the data, a received message, and a lookup. For example, theprocessing module obtains the partial distribution scheme from thesending entity. For instance, the partial distribution scheme indicatesthat an obfuscated partial has been stored in each user device of aplurality of user devices. As another example, the processing moduleobtains the partial distribution scheme based on a DSN memory retrieval.For instance, the partial distribution scheme indicates that allobfuscated partials are stored in the DSN memory.

The method continues at step 260 where the processing module obtainsless than a decode threshold number of obfuscated partials in accordancewith the partial distribution scheme to produce received obfuscatedpartials. The obtaining may include one or more of receiving from thesending entity, retrieving from the DSN memory, and retrieving from oneor more user devices of a plurality of user devices. The methodcontinues at step 262 where the processing module de-obfuscates thereceived obfuscated partial slices to reproduced received partialslices. The method continues at step 264 where the processing modulegenerates a partial slice corresponding to each partial slice of thereceived partial slices in accordance with the encoding scheme toproduce generated partial slices for each slice of the received encodeddata slices. The method continues at step 266 where the processingmodule combines the received partials and the generated partials toproduce one or more recovered encoded data slices. The method continuesat step 268 where the processing module decodes the one or morerecovered encoded data slices and the received encoded data slices toproduce reproduced data in accordance with the encoding scheme.

FIG. 12 is a flowchart illustrating an example of determining parametersof an encoding scheme, which includes similar steps to FIG. 10. Themethod begins at step 270 where a processing module (e.g., of a sendingdispersed storage (DS) processing, of a user device, of a DS processingunit) obtains data to send. The obtaining includes at least one ofretrieving the data, receiving the data, initiating a query with regardsto the data, generating the data, and looking up the data. The methodcontinues at step 272 where the processing module obtains data encodingrequirements. The data encoding requirements includes at least one of asecurity requirement, a bandwidth utilization requirement, a latencyrequirement, a predetermined requirement, a number of receivingentities, and an error coding dispersal storage function parameterrequirement. The obtaining includes at least one of retrieving the dataencoding requirements, receiving the data encoding requirements,initiating a query with respect to the data encoding requirements,generating the data encoding requirements, and looking up the dataencoding requirements.

The method continues at step 274 where the processing module selectsless than a decode threshold number of encoded data slices correspondingto the data to produce selected encoded data slices for subsequentsending based on the data encoding requirements. For example, theprocessing module selects the number of encoded data slices to be onewhen the data encoding requirements indicates to send just one slicebased on a security requirement and the error coding dispersal storagefunction parameters include a pillar width of 5 and a decode thresholdof 3. As another example, the processing module selects the number ofencoded data slices to be two when the data encoding requirementsindicates to send two slices based on a performance requirement and theerror coding dispersal storage function parameters include a pillarwidth of 5 and a decode threshold of 3.

The method continues at step 276 where the processing module selectsanother less than a decode threshold number of encoded data slicescorresponding to the data to produce other selected encoded data slicesto utilize when generating less than a decode threshold number ofpartials for subsequent sending based on the data encoding requirements.For example, the processing module selects encoded data slices 4 and 5as the another encoded data slices when the data encoding requirementsindicates to send just encoded data slice 1 based on a securityrequirement and the error coding dispersal storage function parametersinclude a pillar width of 5 and a decode threshold of 3. As anotherexample, the processing module selects encoded data slice 4 as theanother encoded data slice when the data encoding requirements indicatesto send encoded data slices 1 and 2 based on a performance requirementand the error coding dispersal storage function parameters include apillar width of 5 and a decode threshold of 3.

The method continues at step 278 where the processing module encodes thedata to produce at least a decode threshold number of encoded dataslices corresponding to the selected encoded data slices and the otherselected encoded data slices. For example, the processing module encodesthe data to produce encoded data slices 1, 4, and 5 when the selectedencoded data slices includes encoded data slice 1 and the other selectedencoded data slices includes encoded data slices 4 and 5. As anotherexample, the processing module encodes the data to produce encoded dataslices 1, 2, and 4 when the selected encoded data slices includesencoded data slices 1 and 2 and the other encoded data slices includesencoded data slice 4.

The method continues at step 280 where the processing module generatesat least one partial corresponding to the other selected encoded dataslices. For example, the processing module generates partial slices p(2,4) and p (3,4) corresponding to encoded data slice 4 and theprocessing module generates partial slices p (2,5) and p (3,5)corresponding to encoded data slice 5 when the other selected encodeddata slices includes encoded data slices 4 and 5 and the selectedencoded data slices includes encoded data slice 1. As another example,the processing module generates partial slice p (3,4) corresponding toencoded data slice 4 when the other selected encoded data slicesincludes encoded data slice 4 and the selected encoded data slicesincludes encoded data slices 1 and 2.

The method continues with steps 246 and 250 of FIG. 10 where theprocessing module obfuscates the at least one partial slice to produceat least one obfuscated partial slice and sends the at least oneobfuscated partial slice to at least one receiving entity. The methodcontinues at step 286 where the processing module sends each of the atleast a decode threshold number of encoded data slices except for theother selected encoded data slices to at least one receiving entity. Forexample, the processing module sends encoded data slice 1 when the otherselected encoded data slices includes encoded data slices 4 and 5 andthe selected encoded data slices includes encoded data slice 1. Asanother example, the processing module sends encoded data slices 1 and 2when the other selected encoded data slices includes encoded data slice4 and the selected encoded data slices includes encoded data slices 1and 2.

FIG. 13 is a flowchart illustrating an example of rebuilding an encodeddata slice in error in accordance with the invention, which includessimilar steps to FIG. 11. The method begins at step 288 where aprocessing module (e.g., of a dispersed storage (DS) processing, astorage integrity processing unit, a DS unit, a DS processing unit, auser device) detects an encoded data slice error. The encoded data sliceerror includes at least one of a corrupted encoded data slice, atampered encoded data slice, an encoded data slice that fails anintegrity check, and a missing the encoded data slice. The detection maybe based on one or more of receiving an error message, receiving arebuilding message, a query, and an integrity test.

The method continues at step 290 where the processing module identifiesa least a decode threshold number of user devices associated with atleast a decode threshold number of partial slices corresponding to theencoded data slice error. The identifying includes at least one ofreceiving user device identifiers (IDs), performing a lookup, performinga query, obtaining an encoding scheme, and obtaining a partialdistribution scheme.

The method continues at step 292 where the processing module generatesat least a decode threshold number of partial slice requestscorresponding to the at least a decode threshold number of partialslices. Each partial slice request includes at least one of an encodeddata slice ID, a pillar index, participant pillar IDs, and encodingmatrix, an encoding scheme, a partial distribution scheme, and arequesting entity ID.

The method continues at step 294 where the processing module sends theleast a decode threshold number of partial slice requests to thecorresponding at least a decode threshold number of user devices. Theprocessing module may send a partial slice request directly to a userdevice and/or indirectly via an intermediate user device. For example,the processing module sends partial slice requests to user devices 1,and 3-6. Each partial slice request indicates pillar index 2 and userdevice participants 1, 3-6 when a pillar width is 8 and a decodethreshold is 5. Each user device produces an obfuscated partial slice inresponse to the partial slice request based on at least one of aretrieval from a local memory, a dispersed storage network (DSN) memoryretrieval, and generating the partial slice based on a correspondingstored slice. Each user device may obfuscate the partial slice when thepartial slice is not already obfuscated.

The method continues at step 296 where the processing module receives atleast a decode threshold number of obfuscated partial slices to producereceived obfuscated partial slices. The received obfuscated partialslices may already include combinations (e.g., resulting from anexclusive OR logical function) of two or more obfuscated partial slices.The method continues with step 262 of FIG. 11 where the processingmodule de-obfuscates the received obfuscated partial slices to producereceived partial slices. For example, the processing module may utilizean obfuscation value that includes a unique shared secret with each ofthe plurality of user devices.

The method continues at step 300 where the processing module combinesthe received partial slices to produce a reproduced encoded data slicecorresponding to the encoded data slice error. Alternatively, theprocessing module may simultaneously de-obfuscate the receivedobfuscated partial slices and combine the received partial slices toproduce the reproduced encoded data slice. For example, the processingmodule produces a reproduced encoded data slice 2 utilizing a function:slice 2=(K1)⊕(K1)⊕partial (2,1)⊕(K3)⊕(K3)⊕partial(2,3)⊕(K4)⊕(K4)⊕partial (2,4)⊕(K5)⊕(K5)⊕partial (2,5)⊕(K6)⊕(K6)⊕partial(2,6) when K1 is shared secret obfuscation value associated with userdevice 1 (e.g., (K1)⊕partial(2,1) is received obfuscated partial sliceop (2,1)) and the processing module for regenerating encoded data slice2, K3 is shared secret obfuscation value associated with user device 3and the processing module, K4 is shared secret obfuscation valueassociated with user device 4 and the processing module, K5 is sharedsecret obfuscation value associated with user device 5 and theprocessing module, and K6 is shared secret obfuscation value associatedwith user device 6 and the processing module.

The method continues at step 302 where the processing module facilitatesremedying the encoded data slice error utilizing the reproduced encodeddata slice. The facilitation includes at least one of storing thereproduced encoded data slice in the DSN memory, writing over theencoded data slice error with the reproduced encoded data slice, sendingthe reproduced encoded data slice to a DS unit, sending the reproducedencoded data slice to a user device, and sending the reproduced encodeddata slice to a receiving DS processing.

As may be used herein, the terms “substantially” and “approximately”provides an industry-accepted tolerance for its corresponding termand/or relativity between items.

Such an industry-accepted tolerance ranges from less than one percent tofifty percent and corresponds to, but is not limited to, componentvalues, integrated circuit process variations, temperature variations,rise and fall times, and/or thermal noise. Such relativity between itemsranges from a difference of a few percent to magnitude differences. Asmay also be used herein, the term(s) “operably coupled to”, “coupledto”, and/or “coupling” includes direct coupling between items and/orindirect coupling between items via an intervening item (e.g., an itemincludes, but is not limited to, a component, an element, a circuit,and/or a module) where, for indirect coupling, the intervening item doesnot modify the information of a signal but may adjust its current level,voltage level, and/or power level. As may further be used herein,inferred coupling (i.e., where one element is coupled to another elementby inference) includes direct and indirect coupling between two items inthe same manner as “coupled to”. As may even further be used herein, theterm “operable to” or “operably coupled to” indicates that an itemincludes one or more of power connections, input(s), output(s), etc., toperform, when activated, one or more its corresponding functions and mayfurther include inferred coupling to one or more other items. As maystill further be used herein, the term “associated with”, includesdirect and/or indirect coupling of separate items and/or one item beingembedded within another item. As may be used herein, the term “comparesfavorably”, indicates that a comparison between two or more items,signals, etc., provides a desired relationship. For example, when thedesired relationship is that signal 1 has a greater magnitude thansignal 2, a favorable comparison may be achieved when the magnitude ofsignal 1 is greater than that of signal 2 or when the magnitude ofsignal 2 is less than that of signal 1.

As may also be used herein, the terms “processing module”, “processingcircuit”, and/or “processing unit” may be a single processing device ora plurality of processing devices. Such a processing device may be amicroprocessor, micro-controller, digital signal processor,microcomputer, central processing unit, field programmable gate array,programmable logic device, state machine, logic circuitry, analogcircuitry, digital circuitry, and/or any device that manipulates signals(analog and/or digital) based on hard coding of the circuitry and/oroperational instructions. The processing module, module, processingcircuit, and/or processing unit may be, or further include, memoryand/or an integrated memory element, which may be a single memorydevice, a plurality of memory devices, and/or embedded circuitry ofanother processing module, module, processing circuit, and/or processingunit. Such a memory device may be a read-only memory, random accessmemory, volatile memory, non-volatile memory, static memory, dynamicmemory, flash memory, cache memory, and/or any device that storesdigital information. Note that if the processing module, module,processing circuit, and/or processing unit includes more than oneprocessing device, the processing devices may be centrally located(e.g., directly coupled together via a wired and/or wireless busstructure) or may be distributedly located (e.g., cloud computing viaindirect coupling via a local area network and/or a wide area network).Further note that if the processing module, module, processing circuit,and/or processing unit implements one or more of its functions via astate machine, analog circuitry, digital circuitry, and/or logiccircuitry, the memory and/or memory element storing the correspondingoperational instructions may be embedded within, or external to, thecircuitry comprising the state machine, analog circuitry, digitalcircuitry, and/or logic circuitry. Still further note that, the memoryelement may store, and the processing module, module, processingcircuit, and/or processing unit executes, hard coded and/or operationalinstructions corresponding to at least some of the steps and/orfunctions illustrated in one or more of the Figures. Such a memorydevice or memory element can be included in an article of manufacture.

The present invention has been described above with the aid of methodsteps illustrating the performance of specified functions andrelationships thereof. The boundaries and sequence of these functionalbuilding blocks and method steps have been arbitrarily defined hereinfor convenience of description. Alternate boundaries and sequences canbe defined so long as the specified functions and relationships areappropriately performed. Any such alternate boundaries or sequences arethus within the scope and spirit of the claimed invention. Further, theboundaries of these functional building blocks have been arbitrarilydefined for convenience of description. Alternate boundaries could bedefined as long as the certain significant functions are appropriatelyperformed. Similarly, flow diagram blocks may also have been arbitrarilydefined herein to illustrate certain significant functionality. To theextent used, the flow diagram block boundaries and sequence could havebeen defined otherwise and still perform the certain significantfunctionality. Such alternate definitions of both functional buildingblocks and flow diagram blocks and sequences are thus within the scopeand spirit of the claimed invention. One of average skill in the artwill also recognize that the functional building blocks, and otherillustrative blocks, modules and components herein, can be implementedas illustrated or by discrete components, application specificintegrated circuits, processors executing appropriate software and thelike or any combination thereof.

The present invention may have also been described, at least in part, interms of one or more embodiments. An embodiment of the present inventionis used herein to illustrate the present invention, an aspect thereof, afeature thereof, a concept thereof, and/or an example thereof. Aphysical embodiment of an apparatus, an article of manufacture, amachine, and/or of a process that embodies the present invention mayinclude one or more of the aspects, features, concepts, examples, etc.described with reference to one or more of the embodiments discussedherein. Further, from figure to figure, the embodiments may incorporatethe same or similarly named functions, steps, modules, etc. that may usethe same or different reference numbers and, as such, the functions,steps, modules, etc. may be the same or similar functions, steps,modules, etc. or different ones.

While the transistors in the above described figure(s) is/are shown asfield effect transistors (FETs), as one of ordinary skill in the artwill appreciate, the transistors may be implemented using any type oftransistor structure including, but not limited to, bipolar, metal oxidesemiconductor field effect transistors (MOSFET), N-well transistors,P-well transistors, enhancement mode, depletion mode, and zero voltagethreshold (VT) transistors.

Unless specifically stated to the contra, signals to, from, and/orbetween elements in a figure of any of the figures presented herein maybe analog or digital, continuous time or discrete time, and single-endedor differential. For instance, if a signal path is shown as asingle-ended path, it also represents a differential signal path.Similarly, if a signal path is shown as a differential path, it alsorepresents a single-ended signal path. While one or more particulararchitectures are described herein, other architectures can likewise beimplemented that use one or more data buses not expressly shown, directconnectivity between elements, and/or indirect coupling between otherelements as recognized by one of average skill in the art.

The term “module” is used in the description of the various embodimentsof the present invention. A module includes a processing module, afunctional block, hardware, and/or software stored on memory forperforming one or more functions as may be described herein. Note that,if the module is implemented via hardware, the hardware may operateindependently and/or in conjunction software and/or firmware. As usedherein, a module may contain one or more sub-modules, each of which maybe one or more modules.

While particular combinations of various functions and features of thepresent invention have been expressly described herein, othercombinations of these features and functions are likewise possible. Thepresent invention is not limited by the particular examples disclosedherein and expressly incorporates these other combinations.

What is claimed is:
 1. A method for execution by a processing module ofa computing device, the method comprises: receiving a subset of encodeddata slices of a set of encoded data slices, wherein a data segment ofdata was encoded using an encoding matrix of a dispersed storage errorcoding function to produce the set of encoded data slices, wherein thedata segment can be recreated from a decode threshold number of encodeddata slices of the set of encoded data slices using a decoding matrix ofthe dispersed storage error coding function, wherein the subset ofencoded data slices includes less than the decode threshold number ofencoded data slices of the subset of encoded data slices and does notinclude a first or a second encoded data slice of the set of encodeddata slices; receiving a partial encoded data slice corresponding to thefirst encoded data slice, wherein the partial encoded data slice isgenerated based on the second encoded data slice and a section of theencoding matrix that corresponds to the first encoded data slice;generating additional partial encoded data slices corresponding to thefirst encoded data slice based on the subset of encoded data slices andthe section of the encoding matrix that corresponds to the first encodeddata slice; recreating the first encoded data slice from the partialencoded data slice and the additional partial encoded data slices; anddecoding the subset of encoded data slices and the first encoded dataslice using the decoding matrix to reproduce the data segment.
 2. Themethod of claim 1 further comprises: prior to recreating the firstencoded data slice, de-obfuscating the partial encoded data sliceutilizing an obfuscation function.
 3. The method of claim 1 furthercomprises: the subset of encoded data slices does not include the first,the second, or a third encoded data slice of the set of encoded dataslices, wherein the partial encoded data slice is generated based on thesecond and third encoded data slices and the section of the encodingmatrix that corresponds to the first encoded data slice; receiving asecond partial encoded data slice corresponding to the fourth encodeddata slice, wherein the second partial encoded data slice is generatedbased on the second and the third encoded data slice and a section ofthe encoding matrix that corresponds to the fourth encoded data slice;generating second additional partial encoded data slices correspondingto the fourth encoded data slice based on the subset of encoded dataslices and the section of the encoding matrix that corresponds to thefourth encoded data slice; recreating the fourth encoded data slice fromthe second partial encoded data slice and the second additional partialencoded data slices; and decoding the subset of encoded data slices, thefirst encoded data slice, and the fourth encoded data slice using thedecoding matrix to reproduce the data segment.
 4. The method of claim 1,wherein generating one of the additional partial encoded data slicescomprises: generating a first decoding matrix for the first encoded dataslice based on the encoding matrix; encoding a corresponding one of thesubset of encoded data slices using the first decoding matrix to producea vector; and encoding the vector using, as the section of the encodingmatrix, a row of the encoding matrix that corresponds to the firstencoded data slice to produce the one of the additional partial encodeddata slices.
 5. The method of claim 4, wherein the generating thedecoding matrix comprises: reducing the encoding matrix to produce asquare matrix based on the first encoded data slice and the subset ofencoded data slices; and inverting the square matrix to produce thedecoding matrix.
 6. The method of claim 1, wherein the decoding thesubset of encoded data slices and the first encoded data slicecomprises: generating a received slice matrix from the first encodeddata slice and the subset of encoded data slices; generating a datamatrix based on the received slice matrix and the decoding matrix; andcreating the data segment from the data matrix.
 7. The method of claim 6further comprises: obtaining the encoding matrix; reducing the encodingmatrix based on rows associated with the subset of encoded data slicesand the first encoded data slice to produce a square matrix; andinverting the square matrix to produce the decoding matrix.
 8. Themethod of claim 1, wherein the recreating the first encoded data slicefrom the partial encoded data slice and the additional partial encodeddata slices comprises one of: exclusive ORing the partial encoded dataslice and the additional partial encoded data slices to produce thefirst encoded data slice; and rebuilding the first encoded data slicebased on the partial encoded data slice and the additional partialencoded data slices in accordance with a dispersed storage error codingfunction.
 9. A dispersed storage (DS) module comprises: a first module,when operable within a computing device, causes the computing device to:receive a subset of encoded data slices of a set of encoded data slices,wherein a data segment of data was encoded using an encoding matrix of adispersed storage error coding function to produce the set of encodeddata slices, wherein the data segment can be recreated from a decodethreshold number of encoded data slices of the set of encoded dataslices using a decoding matrix of the dispersed storage error codingfunction, wherein the subset of encoded data slices includes less thanthe decode threshold number of encoded data slices of the subset ofencoded data slices and does not include a first or a second encodeddata slice of the set of encoded data slices; and receive a partialencoded data slice corresponding to the first encoded data slice,wherein the partial encoded data slice is generated based on the secondencoded data slice and a section of the encoding matrix that correspondsto the first encoded data slice; a second module, when operable withinthe computing device, causes the computing device to: generateadditional partial encoded data slices corresponding to the firstencoded data slice based on the subset of encoded data slices and thesection of the encoding matrix that corresponds to the first encodeddata slice; a third module, when operable within the computing device,causes the computing device to: recreate the first encoded data slicefrom the partial encoded data slice and the additional partial encodeddata slices; and a fourth module, when operable within the computingdevice, causes the computing device to: decode the subset of encodeddata slices and the first encoded data slice using the decoding matrixto reproduce the data.
 10. The DS module of claim 9 further comprises:prior to recreating the first encoded data slice, the third modulefurther functions to de-obfuscate the partial encoded data sliceutilizing an obfuscation function.
 11. The DS module of claim 9 furthercomprises: the subset of encoded data slices does not include the first,the second, or a third encoded data slice of the set of encoded dataslices, wherein the partial encoded data slice is generated based on thesecond and third encoded data slices and the section of the encodingmatrix that corresponds to the first encoded data slice; the firstmodule further causes the computing device to receive a second partialencoded data slice corresponding to the fourth encoded data slice,wherein the second partial encoded data slice is generated based on thesecond and the third encoded data slice and a section of the encodingmatrix that corresponds to the fourth encoded data slice; the secondmodule further causes the computing device to generate second additionalpartial encoded data slices corresponding to the fourth encoded dataslice based on the subset of encoded data slices and the section of theencoding matrix that corresponds to the fourth encoded data slice; thethird module further causes the computing device to recreate the fourthencoded data slice from the second partial encoded data slice and thesecond additional partial encoded data slices; and the fourth modulefurther causes the computing device to decode the subset of encoded dataslices, the first encoded data slice, and the fourth encoded data sliceusing the decoding matrix to reproduce the data segment.
 12. The DSmodule of claim 9, wherein the second module functions to generate oneof the additional partial encoded data slices by: generating a firstdecoding matrix for the first encoded data slice based on the encodingmatrix; encoding a corresponding one of the subset of encoded dataslices using the first decoding matrix to produce a vector; and encodingthe vector using, as the section of the encoding matrix, a row of theencoding matrix that corresponds to the first encoded data slice toproduce the one of the additional partial encoded data slices.
 13. TheDS module of claim 12, wherein the second module functions to generatethe decoding matrix by: reducing the encoding matrix to produce a squarematrix based on the first encoded data slice and the subset of encodeddata slices; and inverting the square matrix to produce the decodingmatrix.
 14. The DS module of claim 9, wherein the fourth modulefunctions to decode the subset of encoded data slices and the firstencoded data slice by: generating a received slice matrix from the firstencoded data slice and the subset of encoded data slices; generating adata matrix based on the received slice matrix and the decoding matrix;and creating the data segment from the data matrix.
 15. The DS module ofclaim 14 further comprises: the fourth module further functions to:obtain the encoding matrix; reduce the encoding matrix based on rowsassociated with the subset of encoded data slices and the first encodeddata slice to produce a square matrix; and invert the square matrix toproduce the decoding matrix.
 16. The DS module of claim 9, wherein thethird module functions to recreate the first encoded data slice from thepartial encoded data slice and the additional partial encoded dataslices by one of: exclusive ORing the partial encoded data slice and theadditional partial encoded data slices to produce the first encoded dataslice; and rebuilding the first encoded data slice based on the partialencoded data slice and the additional partial encoded data slices inaccordance with a dispersed storage error coding function.